& {F=\frac{9}{5}(20)+32} \\ {\text { Simplify. }} Show transcribed image text. Since the slope is negative, the final graph of the line should be decreasing when viewed from left to right. & {F=\frac{9}{5} C+32} \\ {\text { Find } F \text { when } C=0 .} 1. Use slopes and $$y$$-intercepts to determine if the lines $$x=−2$$ and $$x=−5$$ are parallel. When we are given an equation in slope–intercept form, we can use the $$y$$-intercept as the point, and then count out the slope from there. A vertical line has an equation of the form x = a, where a is the x-intercept. If the equation is of the form $$Ax+By=C$$, find the intercepts. What is the $$y$$-intercept of the line? C. 3 and + 3 / 4 respectively. Vertical relief wells or pits can be See the answer. Now that we have graphed lines by using the slope and $$y$$-intercept, let’s summarize all the methods we have used to graph lines. C) inversely related. In the above diagram the line crosses the y axis at y = 1. We have used a grid with $$x$$ and $$y$$ both going from about $$−10$$ to $$10$$ for all the equations we’ve graphed so far. D) neither the slope nor the intercept. Use slopes and $$y$$-intercepts to determine if the lines $$y=−4$$ and $$y=3$$ are parallel. D. unrelated. The slope, $$\frac{9}{5}$$, means that the temperature Fahrenheit ($$F$$) increases $$9$$ degrees when the temperature Celsius ($$C$$) increases $$5$$ degrees. B. is 50. The slopes of the lines are the same and the $$y$$-intercept of each line is different. STRATEGY FOR CHOOSING THE MOST CONVENIENT METHOD TO GRAPH A LINE. The slope–intercept form of an equation of a line with slope mm and $$y$$-intercept, $$(0,b)$$ is, $$y=mx+b$$. SLOPE-INTERCEPT FORM OF AN EQUATION OF A LINE. Identify the slope and $$y$$-intercept of both lines. C) the vertical intercept would be negative, but consumption would increase as disposable income rises. We call these lines perpendicular. If we look at the slope of the first line, $$m_{1}=14$$, and the slope of the second line, $$m_{2}=−4$$, we can see that they are negative reciprocals of each other. Graph the line of the equation $$y=0.2x+45$$ using its slope and $$y$$-intercept. Use slopes to determine if the lines $$2x−9y=3$$ and $$9x−2y=1$$ are perpendicular. The slope of the line: ... 135.In the above diagram the vertical intercept and slope are: A)4 and -11/3 respectively. Missed the LibreFest? D. neither the slope nor the intercept. Many students find this useful because of its simplicity. So we know these lines are parallel. When an equation of a line is not given in slope–intercept form, our first step will be to solve the equation for $$y$$. After identifying the slope and $$y$$-intercept from the equation we used them to graph the line. So the slope is useful for the rate at which the loan is being paid back, but it's not the clearest way to figure out how long it took Flynn to pay back the loan. C) inversely related. Plot the y-intercept. Suppose a line has a larger intercept. Since the slope is negative, the final graph of the line should be decreasing when viewed from left to right. The vertical intercept: A)is 40. 2. & {F=36+32} \\ {\text { Simplify. }} The lines have the same slope and different $$y$$-intercepts and so they are parallel. B. directly related. Use the graph to find the slope and $$y$$-intercept of the line, $$y=2x+1$$. Find the cost for a week when she sells $$15$$ pizzas. Since their $$x$$-intercepts are different, the vertical lines are parallel. slope $$m = \frac{2}{3}$$ and $$y$$-intercept $$(0,−1)$$. Now let us see a case where there is no y intercept. We solve the second equation for $$y$$: \begin{aligned} 2x+y &=-1 \\ y &=-2x-1 \end{aligned}. The x-intercept, that's where the graph intersects the horizontal axis, which is often referred to as the x-axis. Count out the rise and run to mark the second point. The slope, $$4$$, means that the cost increases by $$4$$ for each pizza Stella sells. In economics, the slope … The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Slope Intercept Equation of Vertical and Horizontal lines Vertical Lines. Use slopes to determine if the lines $$y=2x−5$$ and $$x+2y=−6$$ are perpendicular. Even though this equation uses $$F$$ and $$C$$, it is still in slope–intercept form. Since a vertical line goes straight up and down, its slope is undefined. Find Loreen’s cost for a week when she writes no invitations. I can write equations of lines using y=mx+b. B) directly related. The slopes are negative reciprocals of each other, so the lines are perpendicular. Compare these values to the equation $$y=mx+b$$. Substituting into the slope formula: \begin{aligned} m &=\frac{\text { rise }}{\text { rise }} \\ m &=\frac{1}{2} \end{aligned}. I know that the slope is m = {{ - 5} \over 3} and the y-intercept is b = 3 or \left( {0,3} \right). Often, especially in applications with real-world data, we’ll need to extend the axes to bigger positive or smaller negative numbers. The vertical intercept: A. is 40. The lines have the same slope and different $$y$$-intercepts and so they are parallel. Graph the line of the equation $$y=0.5x+25$$ using its slope and $$y$$-intercept. The first equation is already in slope–intercept form: $$\quad y=−5x−4$$ 3 and -1 … C) both the slope and the intercept. 3. The lines have the same slope, but they also have the same $$y$$-intercepts. B. is 50. Determine the most convenient method to graph each line. This useful form of the line equation is sensibly named the "slope-intercept form". The second equation is now in slope–intercept form as well. If $$y$$ is isolated on one side of the equation, in the form $$y=mx+b$$, graph by using the slope and $$y$$-intercept. What is the slope of each line? -intercept.Jada's graph has a vertical intercept of $20 while Lin's graph has a vertical intercept of$ 10. & {F=32}\end{array}\), 2. In the above diagram the vertical intercept and slope are: A. Let’s graph the equations $$y=−2x+3$$ and $$2x+y=−1$$ on the same grid. We say that vertical lines that have different $$x$$-intercepts are parallel. You can only see part of the lines, but they actually continue forever in both directions. This example illustrates how the b and m terms in an equation for a straight line determine the position of the line on a graph. Use slopes and $$y$$-intercepts to determine if the lines $$y=\frac{3}{4}x−3$$ and $$3x−4y=12$$ are parallel. Graph a Line Using its Slope and y-Intercept. Horizontal & vertical lines. The cost of running some types business has two components—a fixed cost and a variable cost. & {y=2x-3}&{}&{} \\ \\ {\text { Solve the second equation for } y} & {-6x+3y} &{=}&{-9} \\{} & {3y}&{=}&{6x-9} \\ {}&{\frac{3y}{3} }&{=}&{\frac{6x-9}{3}} \\{} & {y}&{=}&{2x-3}\end{array}\). 4 and -1 1 / 3 respectively. Starting at the $$y$$-intercept, count out the rise and run to mark the second point. B) one. The slope–intercept form of an equation of a line with slope mm and $$y$$-intercept, $$(0,b)$$ is, Sometimes the slope–intercept form is called the “y-form.”. Refer to the above diagram. Identify the slope and $$y$$-intercept of the line with equation $$y=−3x+5$$. We say that the equation $$y=\frac{1}{2}x+3$$ is in slope–intercept form. Write the slope–intercept form of the equation of the line. This problem has been solved! B) 3 and -1 1 / 3 respectively. You may want to graph the lines to confirm whether they are parallel. The slope, $$2$$, means that the height, $$h$$, increases by $$2$$ inches when the shoe size, $$s$$, increases by $$1$$. Also, the x value of every point on a vertical line is the same. Graphically, that means it would shift out (or up) from the old origin, parallel to … The slope of a vertical line is undefined, so vertical lines don’t fit in the definition above. ... in each diagram: Select all the pairs of points so that the line between those points has slope . On the basis of this information we can say that: Use the following to answer questions 149-151: Refer to the above diagram. The y-intercept is an (x,y) point with x=0, so we show it like this (try dragging the points): Equation of a Straight Line Gradient (Slope) of a Straight Line Test Yourself Straight Line Graph Calculator Graph Index. B) the slope would be -7.5. 4 and -1 1/3 respectively. At every point on the line, AE measured on the vertical axis equals current output, Y, measured on the horizontal axis. D) cannot be determined from the information given. This is always true for perpendicular lines and leads us to this definition. We’ll use the points $$(0,1)$$ and $$(1,3)$$. Well, you can think about what's the slope as you approach this but once again, that could be, some people would say, maybe it's infinite, maybe it's negative infinity. Use the slope formula to identify the rise and the run. & {y}&{=m x+b} &{y}&{=}&{m x+b} \\{} & {m_{1}} & {=-\frac{7}{2} }&{ m_{2}}&{=}&{-\frac{2}{7}}\end{array}\). 4. The intercept at any point is positive if it lies above the tangent, negative if the it is below the tangent. Also notice that this is the value of b in the linear function f(x) = mx + b. &{y=0 x-4} & {} &{y=0 x+3} \\ {\text{Identify the slope and }y\text{-intercept of both lines.}} Graph the line of the equation $$y=2x−3$$ using its slope and $$y$$-intercept. Let’s practice finding the values of the slope and $$y$$-intercept from the equation of a line. $$\begin{array}{ll}{\text { Find the Fahrenheit temperature for a Celsius temperature of } 0 .} See Figure \(\PageIndex{1}$$. In equations #3 and #4, both $$x$$ and $$y$$ are on the same side of the equation. Estimate the height of a child who wears women’s shoe size $$0$$. 8.1 Lines that Are Translations. I can explain where to find the slope and vertical intercept in both an equation and its graph. I know that the slope is m = {{ - 5} \over 3} and the y-intercept is b = 3 or \left( {0,3} \right). The 45° line labeled $$Y = \text{AE}$$, illustrates the equilibrium condition. Use slopes and $$y$$-intercepts to determine if the lines $$x=8$$ and $$x=−6$$ are parallel. &{ 3 x-2 y} &{=} &{6}\\{} & {\frac{-2 y}{-2}} &{ =}&{-3 x+6 }\\ {} &{\frac{-2 y}{-2}}&{ =}&{\frac{-3 x+6}{-2}} \\ {} & {y }&{=}&{\frac{3}{2} x-3} \end{array}\). Identify the slope and y-intercept. Since f(0) = -7.2(0) + 250 = 250, the vertical intercept is 250. and P is its price. Estimate the temperature when the number of chirps in one minute is $$100$$. &{7 x+2 y} & {=3} & {2 x+7 y}&{=}&{5} \\{} & {2 y} & {=-7 x+3} & {7 y}&{=}&{-2 x+5} \\ {} &{\frac{2 y}{2}} & {=\frac{-7 x+3}{2} \quad} & {\frac{7 y}{7}}&{=}&{\frac{-2 x+5}{7}} \\ {} &{y} & {=-\frac{7}{2} x+\frac{3}{2}} &{y}&{=}&{\frac{-2}{7}x + \frac{5}{7}}\\ \\{\text{Identify the slope of each line.}} Now that we have seen several methods we can use to graph lines, how do we know which method to use for a given equation? Use the graph to find the slope and $$y$$-intercept of the line $$y=\frac{1}{2}x+3$$. We can do the same thing for perpendicular lines. Graph the line of the equation $$y=−\frac{3}{4}x−2$$ using its slope and $$y$$-intercept. This means that the graph of the linear function crosses the horizontal axis at the point (0, 250). D. … The slope of curve ZZ at point B is: Refer to the above diagram. The slope of a vertical line is undefined, so vertical lines don’t fit in the definition above. They are not parallel; they are the same line. Find the cost for a week when he drives $$250$$ miles. The diagram shows several lines. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. This preview shows page 6 - 9 out of 54 pages. Course Hero is not sponsored or endorsed by any college or university. While we could plot points, use the slope–intercept form, or find the intercepts for any equation, if we recognize the most convenient way to graph a certain type of equation, our work will be easier. Have questions or comments? The slope and y-intercept calculator takes a linear equation and allows you to calculate the slope and y-intercept for the equation. Once we see how an equation in slope–intercept form and its graph are related, we’ll have one more method we can use to graph lines. Use the slope formula $$\frac{\text{rise}}{\text{run}}$$ to identify the rise and the run. We'll need to use a larger scale than our usual. In Graph Linear Equations in Two Variables, we graphed the line of the equation $$y=12x+3$$ by plotting points. slope $$m = \frac{1}{2}$$ and $$y$$-intercept $$(0,3)$$. Legal. The $$y$$-intercept is where the line crosses the $$y$$-axis, so $$y$$-intercept is $$(0,3)$$. See Figure $$\PageIndex{2}$$. Answer: D 37. Expert Answer . This means that the graph of the linear function crosses the horizontal axis at the point (0, 250). Equations of this form have graphs that are vertical or horizontal lines. The vertical intercept: A. is 40. In a valley, barriers within 8 to 20 inches of the soil surface often cause a perched water table above the true water table. The slope of curve ZZ at point A is approximately: A. Use the following to answer questions 30-32: 30. The equation of the second line is already in slope–intercept form. 3 and … We were able to look at the slope–intercept form of linear equations and determine whether or not the lines were parallel. These two equations are of the form $$Ax+By=C$$. We compare our equation to the slope–intercept form of the equation. 152. Parallel lines have the same slope and different $$y$$-intercepts. & {F=68}\end{array}. &{y=m x+b} &{} & {y=m x+b} \\ {} &{m=0} &{} & {m=0} \\{} & {y\text {-intercept is }(0,4)} &{} & {y \text {-intercept is }(0,3)}\end{array}\). Also notice that this is the value of b in the linear function f(x) = mx + b. The slope of a line indicates how steep the line is and whether it rises or falls as we read it from left to right. The equation of this line is: When a linear equation is solved for $$y$$, the coefficient of the $$x$$-term is the slope and the constant term is the $$y$$-coordinate of the $$y$$-intercept. The m in the equation is the slope … Though we can easily just connect the X and Y intercepts to find the budget line representing all possible combinations that expend José’s entire budget, it is important to discuss what the slope of this line represents. C. both the slope and the intercept. $$\begin{array}{lll}{y=\frac{3}{2} x+1} & {} & {y=\frac{3}{2} x-3} \\ {y=m x+b} & {} & {y=m x+b}\\ {m=\frac{3}{2}} & {} & {m=\frac{3}{2}} \\ {y\text{-intercept is }(0, 1)} & {} & {y\text{-intercept is }(0, −3)} \end{array}$$. If $$m_{1}$$ and $$m_{2}$$ are the slopes of two parallel lines then $$m_{1} = m_{2}$$. $\begin{array}{lll}{y=2x-3} &{} & {y=2x-3} \\ {y=mx+b} &{} & {y=mx+b} \\ {m=2} &{} & {m=2} \\ {\text{The }y\text{-intercept is }(0 ,−3)} &{} & {\text{The }y\text{-intercept is }(0 ,−3)} \end{array} \nonumber$. &{x-5y} &{=} &{5} \\{} &{-5 y} &{=} &{-x+5} \\ {} & {\frac{-5 y}{-5}} &{=} &{\frac{-x+5}{-5}} \\ {} &{y} &{=} &{\frac{1}{5} x-1} \end{array}\). Identify the slope and $$y$$-intercept of the line $$3x+2y=12$$. $\begin{array}{c}{m_{1} \cdot m_{2}} \\ {\frac{1}{4}(-4)} \\ {-1}\end{array}$. Remember, in equations of this form the value of that one variable is constant; it does not depend on the value of the other variable. 115.Refer to the above diagram. Formula. The break-even level of disposable income: A) is zero. Does it make sense to you that the slopes of two perpendicular lines will have opposite signs? It only has a y intercept as (0,-2). Perpendicular lines are lines in the same plane that form a right angle. 1. Use slopes and $$y$$-intercepts to determine if the lines $$2x+5y=5$$ and $$y=−\frac{2}{5}x−4$$ are parallel. $$y=−6$$ D) unrelated. Slope of a horizontal line (Opens a modal) Horizontal & vertical lines (Opens a modal) Practice. $$\begin{array}{llll}{\text{Write each equation in slope-intercept form.}} Use slopes and \(y$$-intercepts to determine if the lines $$3x−2y=6$$ and $$y = \frac{3}{2}x + 1$$ are parallel. A vertical line has an equation of the form x = a, where a is the x-intercept. Find Sam’s cost for a week when he drives $$0$$ miles. If you recognize right away from the equations that these are horizontal lines, you know their slopes are both $$0$$. Use slopes and $$y$$-intercepts to determine if the lines $$y=2x−3$$ and $$−6x+3y=−9$$ are parallel. Refer to the above diagram. Find the cost for a week when she sells $$15$$ pizzas. D) 4 and + 3 / 4 respectively. +2 1 / 2. Use slopes and $$y$$-intercepts to determine if the lines $$4x−3y=6$$ and $$y=\frac{4}{3}x−1$$ are parallel. We saw better methods in sections 4.3, 4.4, and earlier in this section. $$x=a$$ is a vertical line passing through the $$x$$-axis at $$a$$. Since parallel lines have the same slope and different $$y$$-intercepts, we can now just look at the slope–intercept form of the equations of lines and decide if the lines are parallel. Remember, you want to do what's your change in y or change in x. In the graph we see the line goes through $$(4, 0)$$. $$\begin{array} {lrllllll} {\text{Identify the slope of each line.}} The slope is the same as the coefficient of \(x$$ and the $$y$$-coordinate of the $$y$$-intercept is the same as the constant term. To find the intersection of two straight lines: First we need the equations of the two lines. Compare these values to the equation $$y=mx+b$$. One can easily describe the characteristics of the straight line even without seeing its graph because the slope and y-intercept can easily be identified. See Figure $$\PageIndex{5}$$. Given the scale of our graph, it would be easier to use the equivalent fraction $$m=\frac{10}{50}$$. Let’s look at the lines whose equations are $$y=\frac{1}{4}x−1$$ and $$y=−4x+2$$, shown in Figure $$\PageIndex{5}$$. Graph the line of the equation $$2x−y=6$$ using its slope and $$y$$-intercept. with the land slope, toward an outlet. Start at the $$F$$-intercept $$(0,32)$$ then count out the rise of $$9$$ and the run of $$5$$ to get a second point. The $$h$$-intercept means that when the shoe size is $$0$$, the height is $$50$$ inches. C. inversely related. 4 And +3/4 Respectively. Horizontal & vertical lines Get 5 of 7 questions to level up! $\begin{array}{lll} {y} & {=m x+b} & {y=m x+b} \\ {y} & {=-2 x+3} & {y=-2 x-1} \\ {m} & {=-2} & {m=-2}\\ {b} & {=3,(0,3)} & {b=-1,(0,-1)}\end{array}$. Recognize the relation between the graph and the slope–intercept form of an equation of a line, Identify the slope and y-intercept form of an equation of a line, Graph a line using its slope and intercept, Choose the most convenient method to graph a line, Graph and interpret applications of slope–intercept, Use slopes to identify perpendicular lines. 160. Find the cost for a week when she writes $$75$$ invitations. Intercept = y mean – slope* x mean. Vertical lines and horizontal lines are always perpendicular to each other. The Keynesian cross diagram depicts the equilibrium level of national income in the G&S market model. So I would rule that one out. Learn. The $$T$$-intercept means that when the number of chirps is $$0$$, the temperature is $$40°$$. What do you notice about the slopes of these two lines? D) one-half. The equation is now in slope–intercept form. Refer to the above diagram. Identify the slope and $$y$$-intercept of the line with equation $$x+2y=6$$. B. 159. Parallel lines are lines in the same plane that do not intersect. Refer to the above diagram. Learn about the slope-intercept form of two-variable linear equations, and how to interpret it to find the slope and y-intercept of their line. Find the slope-intercept form of the equation of the line. 114.Refer to the above diagram. Identify the slope and $$y$$-intercept of the line $$y=−\frac{4}{3}x+1$$. 4. Their $$x$$-intercepts are $$−2$$ and $$−5$$. There is only one variable, $$x$$. If $$m_1$$ and $$m_2$$ are the slopes of two parallel lines then $$m_1 = m_2$$. 3. +2. Slope. The graph is a vertical line crossing the $$x$$-axis at $$7$$. Stella has a home business selling gourmet pizzas. The slopes are reciprocals of each other, but they have the same sign. To check your work, you can find another point on the line and make sure it is a solution of the equation. C. inversely related. Graph the line of the equation $$3x−2y=8$$ using its slope and $$y$$-intercept. B) the intercept only. Answer: C 145. The 45° line labeled $$Y = \text{AE}$$, illustrates the equilibrium condition. In the above diagram variables x and y are: A. both dependent variables. In the above diagram variables x and y are: In the above diagram the vertical intercept and slope are: In the above diagram the equation for this line is: Consumers want to buy pizza is given equation P = 15 - .02Q. persists because economic wants exceed available productive resources. Graph the line of the equation $$y=4x−2$$ using its slope and $$y$$-intercept. Perpendicular lines may have the same $$y$$-intercepts. The $$y$$-intercept is the point $$(0, 1)$$. B) directly related. Sam drives a delivery van. What about vertical lines? B. The equation $$C=0.5m+60$$ models the relation between his weekly cost, $$C$$, in dollars and the number of miles, $$m$$, that he drives. $$x=7$$ Question: 5 4 3 2 1 2 345 In The Diagram, The Vertical Intercept And Slope Are 3 And +3/4 Respectively. $$\begin{array} {llll} {\text{Solve the second equation for }y.} \(y=b$$ is a horizontal line passing through the $$y$$-axis at $$b$$. 31. 3 and -1 … We find the slope–intercept form of the equation, and then see if the slopes are negative reciprocals. \begin{array}{ll}{\text { Find the Fahrenheit temperature for a Celsius temperature of } 20 .} Two lines that have the same slope are called parallel lines. C. inversely related. $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$, 3.5: Use the Slope–Intercept Form of an Equation of a Line, [ "article:topic", "slope-intercept form", "license:ccbyncsa", "transcluded:yes", "source-math-15147" ], https://math.libretexts.org/@app/auth/2/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FCourses%2FHighline_College%2FMath_084_%25E2%2580%2593_Intermediate_Algebra_Foundations_for_Soc_Sci%252C_Lib_Arts_and_GenEd%2F03%253A_Graphing_Lines_in_Two_Variables%2F3.05%253A_Use_the_SlopeIntercept_Form_of_an_Equation_of_a_Line, $$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$, Recognize the Relation Between the Graph and the Slope–Intercept Form of an Equation of a Line, Identify the Slope and $$y$$-Intercept From an Equation of a Line, Graph a Line Using its Slope and Intercept, Choose the Most Convenient Method to Graph a Line, Graph and Interpret Applications of Slope–Intercept, Use Slopes to Identify Perpendicular Lines, Explore the Relation Between a Graph and the Slope–Intercept Form of an Equation of a Line. One can determine the amount of any level of total income that is consumed by: A) multiplying total income by the slope of the consumption schedule. Since this equation is in $$y=mx+b$$ form, it will be easiest to graph this line by using the slope and $$y$$-intercept. Since there is no $$y$$, the equations cannot be put in slope–intercept form. Interpret the slope and $$F$$-intercept of the equation. $$m = -\frac{2}{3}$$; $$y$$-intercept is $$(0, −3)$$. D. neither the slope nor the intercept. Figure 6.9: The 45° Diagram and Equilibrium GDP The 45° line gives Y = AE the equilibrium condition. Answer: B 11. Estimate the temperature when there are no chirps. At 1 week they will have saved the same amount, $30. Their equations represent the same line. 5. 4 and -1 1/3 respectively. Step 1: Begin by plotting the y-intercept of the given equation which is \left( {0,3} \right). D. cannot be determined from the information given. Figure 6.9: The 45° Diagram and Equilibrium GDP The 45° line gives Y = AE the equilibrium condition. Estimate the height of a woman with shoe size $$8$$. $$y=\frac{2}{5}x−1$$ B. the intercept only. Generally, plotting points is not the most efficient way to graph a line. The slope of curve ZZ at point A is: Refer to the above diagram. The m term in the equation for the line is the slope. Loreen has a calligraphy business. Equations #1 and #2 each have just one variable. Graph the line of the equation $$y=−\frac{5}{2}x+1$$ using its slope and $$y$$-intercept. The fixed cost is always the same regardless of how many units are produced. Here are six equations we graphed in this chapter, and the method we used to graph each of them. In addition, not all graphs have both horizontal and vertical intercepts. Let us use these relations to determine the linear regression for the above dataset. In the above diagram variables x and y are: A) both dependent variables. In this article, we will mostly talk about straight lines, but the intercept points can be calculated … The variable names remind us of what quantities are being measured. Use slopes and $$y$$-intercepts to determine if the lines $$x=1$$ and $$x=−5$$ are parallel. The Equation of a vertical line is x = b. After 4 miles, the elevation is 6200 feet above sea level. At every point on the line, AE measured on the vertical axis equals current output, Y, measured on the horizontal axis. A vertical line has an undefined slope. B) directly related. B. 161. Well, it's undefined. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. We say that vertical lines that have different $$x$$-intercepts are parallel. In the above diagram the vertical intercept and slope are: A) 4 and -1 1 / 3 respectively. Find Stella’s cost for a week when she sells no pizzas. We will take a look at a few applications here so you can see how equations written in slope–intercept form relate to real-world situations. The variable cost depends on the number of units produced. To find the slope of the line, we need to choose two points on the line. C) is$100. $$\begin{array} {llll} {\text { The first equation is already in slope-intercept form. }} The \(C$$-intercept means that even when Stella sells no pizzas, her costs for the week are $$25$$. has been solved in all industrialized nations. Identify the rise and the run; count out the rise and run to mark the second point. The slope, $$0.5$$, means that the weekly cost, $$C$$, increases by $$0.50$$ when the number of miles driven, $$n$$, increases by $$1$$. (Remember: $$\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$$). Interpret the slope and $$h$$-intercept of the equation. We begin with a plot of the aggregate demand function with respect to real GNP (Y) in Figure 8.8.1 .Real GNP (Y) is plotted along the horizontal axis, and aggregate demand is measured along the vertical axis.The aggregate demand function is shown as the upward sloping line labeled AD(Y, …). Determine the most convenient method to graph each line: Many real-world applications are modeled by linear equations. Refer to the above diagram. Equation of a line The slope m of a line is one of the elements in the equation of a line when written in the "slope and intercept" form: y = mx+b. Since they are not negative reciprocals, the lines are not perpendicular. O 3 And -11/3 Respectively O 4 And -11/3 Respectively. This equation is not in slope–intercept form. The equation $$T=\frac{1}{4}n+40$$ is used to estimate the temperature in degrees Fahrenheit, $$T$$, based on the number of cricket chirps, $$n$$, in one minute. $$\begin{array}{lrlrl}{\text{Solve the equations for y.}} Since f(0) = -7.2(0) + 250 = 250, the vertical intercept is 250. Refer to the above diagram. 152. Find the Fahrenheit temperature for a Celsius temperature of \(20$$. $\begin{array}{lll}{\text{#1}}&{\text {Equation }} & {\text { Method }} \\ {\text{#2}}&{x=2} & {\text { Vertical line }} \\ {\text{#3}}&{y=4} & {\text { Hortical line }} \\ {\text{#4}}&{-x+2 y=6} & {\text { Intercepts }} \\ {\text{#5}}&{4 x-3 y=12} & {\text { Intercepts }} \\ {\text{#6}}&{y=4 x-2} & {\text { Slope-intercept }} \\{\text{#7}}& {y=-x+4} & {\text { Slope-intercept }}\end{array}$. −1\ ) long lines across the slope of a horizontal line. } 0, 250.! 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