# in the above diagram the vertical intercept and slope are

The slope of the line: ... 135.In the above diagram the vertical intercept and slope are: A)4 and -11/3 respectively. B. is 50. In order to compare it to the slope–intercept form we must first solve the equation for \(y\). Use slopes and \(y\)-intercepts to determine if the lines \(x=−2\) and \(x=−5\) are parallel. \(m = -\frac{2}{3}\); \(y\)-intercept is \((0, −3)\). B. & {F=\frac{9}{5}(20)+32} \\ {\text { Simplify. }} See Figure \(\PageIndex{1}\). Therefore, whatever the x value is, is also the value of 'b'. The slope and y-intercept calculator takes a linear equation and allows you to calculate the slope and y-intercept for the equation. On the basis of this information we can say that: Use the following to answer questions 149-151: Refer to the above diagram. 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. 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. Since there is no \(y\), the equations cannot be put in slope–intercept form. Step 1: Begin by plotting the y-intercept of the given equation which is \left( {0,3} \right). Find Loreen’s cost for a week when she writes no invitations. \(\begin{array} {lrllllll} {\text{Identify the slope of each line.}} What is the \(y\)-intercept of the line? Determine the most convenient method to graph each line. So we know these lines are parallel. The variable names remind us of what quantities are being measured. D. 4 and + 3 / 4 respectively. D) the vertical intercept would be +20 and the slope would be +.6. & {F=\frac{9}{5} C+32} \\ {\text { Find } F \text { when } C=0 .} In the above diagram the vertical intercept and slope are: A. In the above diagram the vertical intercept and slope are: A) 4 and … A negative slope that is larger in absolute value (that is, more negative) means a steeper downward tilt to the line. 4 and -1 1/3 respectively. 8.1 Lines that Are Translations. See the answer. B. directly related. Find the slope–intercept form of the equation. They are not parallel; they are the same line. The graph is a vertical line crossing the \(x\)-axis at \(7\). 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. Find the cost for a week when she writes \(75\) invitations. Now let us see a case where there is no y intercept. and P is its price. Graph the line of the equation \(y=4x−2\) using its slope and \(y\)-intercept. The easiest way to graph it will be to find the intercepts and one more point. To find the intersection of two straight lines: First we need the equations of the two lines. 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. Let’s graph the equations \(y=−2x+3\) and \(2x+y=−1\) on the same grid. Let us use these relations to determine the linear regression for the above dataset. \[\begin{array}{lll} {y} & {=m x+b} & {y=m x+b} \\ {y} & {=-2 x+3} & {y=-2 x-1} \\ {m} & {=-2} & {m=-2}\\ {b} & {=3,(0,3)} & {b=-1,(0,-1)}\end{array}\]. Find Stella’s cost for a week when she sells no pizzas. The m in the equation is the slope … Vertical lines and horizontal lines are always perpendicular to each other. C) inversely related. Start at the \(C\)-intercept \((0, 25)\) then count out the rise of \(4\) and the run of \(1\) to get a second point. For more on this see Slope of a vertical line. See Figure \(\PageIndex{5}\). The slope, \(1.8\), means that the weekly cost, \(C\), increases by \($1.80\) when the number of invitations, \(n\), increases by \(1.80\). B) 3 and -1 1 / 3 respectively. This is always true for perpendicular lines and leads us to this definition. C) 3 and + 3 / 4 respectively. Parallel vertical lines have different \(x\)-intercepts. Stella's fixed cost is \($25\) when she sells no pizzas. 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. \(y=b\) is a horizontal line passing through the \(y\)-axis at \(b\). C. inversely related. 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. If \(m_1\) and \(m_2\) are the slopes of two perpendicular lines, then \(m_1\cdot m_2=−1\) and \(m_1=\frac{−1}{m_2}\). 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. 152. Since they are not negative reciprocals, the lines are not perpendicular. See Figure \(\PageIndex{2}\). B. is 50. B. directly related. B. the intercept only. C)is 60. Answer: A 6 Slope of a horizontal line (Opens a modal) Horizontal & vertical lines (Opens a modal) Practice. 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. In the above diagram variables x and y are: A) both dependent variables. D) unrelated. Step 2: Click the blue arrow to submit and see the result! 2. & {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}\). To find the slope of the line, we need to choose two points on the line. This means that the graph of the linear function crosses the horizontal axis at the point (0, 250). Answer: D 37. See Figure \(\PageIndex{5}\). Not all linear equations can be graphed on this small grid. The diagram shows several lines. If the product of the slopes is \(−1\), the lines are perpendicular. Refer to the above diagram. This useful form of the line equation is sensibly named the "slope-intercept form". Find the cost for a week when she sells \(15\) pizzas. STRATEGY FOR CHOOSING THE MOST CONVENIENT METHOD TO GRAPH A LINE. Remember, the slope is the rate of change. At every point on the line, AE measured on the vertical axis equals current output, Y, measured on the horizontal axis. We'll need to use a larger scale than our usual. The equation \(F=\frac{9}{5}C+32\) is used to convert temperatures, \(C\), on the Celsius scale to temperatures, \(F\), on the Fahrenheit scale. The \(C\)-intercept means that even when Stella sells no pizzas, her costs for the week are \($25\). Well, it's undefined. Use the slope formula \(m = \dfrac{\text{rise}}{\text{run}}\) to identify the rise and the run. In Understand Slope of a Line, we graphed a line using the slope and a point. Since a vertical line goes straight up and down, its slope is undefined. 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. A vertical line has an equation of the form x = a, where a is the x-intercept. 114.Refer to the above diagram. Since the horizontal lines cross the \(y\)-axis at \(y=−4\) and at \(y=3\), we know the \(y\)-intercepts are \((0,−4)\) and \((0,3)\). Graph the line of the equation \(y=0.2x+45\) using its slope and \(y\)-intercept. After identifying the slope and \(y\)-intercept from the equation we used them to graph the line. 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. +2. The line \(y=−4x+2\) drops from left to right, so it has a negative slope. For more on this see Slope of a vertical line. Many students find this useful because of its simplicity. Access this online resource for additional instruction and practice with graphs. For example: The horizontal line graphed above does not have an x intercept. In the above diagram variables x and y are A both dependent variables B, 80 out of 88 people found this document helpful. 1. D. … Stella has a home business selling gourmet pizzas. Interpret the slope and \(C\)-intercept of the equation. If you're seeing this message, it means we're having trouble loading external resources on our website. The \(C\)-intercept means that when the number of invitations is \(0\), the weekly cost is \($35\). Identify the slope and \(y\)-intercept of the line \(3x+2y=12\). Find the cost for a week when he drives \(250\) miles. \(\begin{array}{ll}{\text { Find the Fahrenheit temperature for a Celsius temperature of } 0 .} Use slopes to determine if the lines \(y=2x−5\) and \(x+2y=−6\) are perpendicular. This preview shows page 6 - 9 out of 54 pages. Equations of this form have graphs that are vertical or horizontal lines. Perpendicular lines may have the same \(y\)-intercepts. C. is 60. What do you notice about the slopes of these two lines? In the above diagram the vertical intercept and slope are: A. Refer to the above diagram. Graph the line of the equation \(3x−2y=8\) using its slope and \(y\)-intercept. C) it would graph as a downsloping line. The slope-intercept form is the most "popular" form of a straight line. &{y=-4} & {\text { and }} &{ y=3} \\ {\text{Since there is no }x\text{ term we write }0x.} As we read from left to right, the line \(y=14x−1\) rises, so its slope is positive. C. both the slope and the intercept. D) one-half. Let’s look at the lines whose equations are \(y=\frac{1}{4}x−1\) and \(y=−4x+2\), shown in Figure \(\PageIndex{5}\). Refer to the above diagram. 3 and -1 … B. Graph the line of the equation \(y=0.1x−30\) using its slope and \(y\)-intercept. If we multiply them, their product is \(−1\). This is the cost of rent, insurance, equipment, advertising, and other items that must be paid regularly. If it only has one variable, it is a vertical or horizontal line. The equation can be in any form as long as its linear and and you can find the slope and y-intercept. We check by multiplying the slopes, \[\begin{array}{l}{m_{1} \cdot m_{2}} \\ {-5\left(\frac{1}{5}\right)} \\ {-1\checkmark}\end{array}\]. Sam drives a delivery van. Use slopes and \(y\)-intercepts to determine if the lines \(4x−3y=6\) and \(y=\frac{4}{3}x−1\) are parallel. We’ll use a grid with the axes going from about \(−80\) to \(80\). & {F=32}\end{array}\), 2. Use the graph to find the slope and \(y\)-intercept of the line \(y=\frac{2}{3}x−1\). The lines have the same slope and different \(y\)-intercepts and so they are parallel. Since f(0) = -7.2(0) + 250 = 250, the vertical intercept is 250. 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. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. C. inversely related. 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? At 1 week they will have saved the same amount, $ 30. The \(T\)-intercept means that when the number of chirps is \(0\), the temperature is \(40°\). Identify the slope and \(y\)-intercept and then graph. These values reflect the amount of money they each started with. 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. 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. \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\), 3.5: Use the Slope–Intercept Form of an Equation of a Line, [ "article:topic", "slope-intercept form", "license:ccbyncsa", "transcluded:yes", "source[1]-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, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\), 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. We have graphed linear equations by plotting points, using intercepts, recognizing horizontal and vertical lines, and using the point–slope method. University of Nebraska, Lincoln • ECON 212, Chandler-Gilbert Community College • ECON 001-299, Johnson County Community College • ECON 230, University of Nebraska, Kearney • ECON 270, University of Southern California • ECON 203. &{y} &{=} &{-5 x-4} & {} &{y} &{=} &{\frac{1}{5} x-1} \\ {} &{y} &{=} &{m x+b} & {} &{y} &{=} &{m x+b}\\ {} &{m_{1}} &{=}&{-5} & {} &{m_{2}} &{=}&{\frac{1}{5}}\end{array}\). Substituting into the slope formula: \[\begin{aligned} m &=\frac{\text { rise }}{\text { rise }} \\ m &=\frac{1}{2} \end{aligned}\]. Use slopes and \(y\)-intercepts to determine if the lines \(y=−4\) and \(y=3\) are parallel. 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, …). The m term in the equation for the line is the slope. Estimate the temperature when the number of chirps in one minute is \(100\). The slope–intercept form of an equation of a line with slope and y-intercept, is, . &{x-5y} &{=} &{5} \\{} &{-5 y} &{=} &{-x+5} \\ {} & {\frac{-5 y}{-5}} &{=} &{\frac{-x+5}{-5}} \\ {} &{y} &{=} &{\frac{1}{5} x-1} \end{array}\). Parallel lines never intersect. A slope of zero is a horizontal flat line. 1. 159. It only has a y intercept as (0,-2). Isolated seeps at elevations above the drain can be tapped with stub relief drains to avoid additional long lines across the slope. The equation \(C=4p+25\) models the relation between her weekly cost, \(C\), in dollars and the number of pizzas, \(p\), that she sells. Slope calculator, formula, work with steps, practice problems and real world applications to learn how to find the slope of a line that passes through A and B in geometry. Use the slope formula to identify the rise and the run. In the above diagram the vertical intercept and slope are: A. 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. Use slopes to determine if the lines \(2x−9y=3\) and \(9x−2y=1\) are perpendicular. The car example above is a very simple one that should help you understand why the slope intercept form is important and more specifically, the meaning of the intercepts. The \(y\)-intercept is the point \((0, 1)\). The equation \(C=1.8n+35\) models the relation between her weekly cost, \(C\), in dollars and the number of wedding invitations, \(n\), that she writes. B)is 50. 3 and -1 … Use slopes and \(y\)-intercepts to determine if the lines \(y=8\) and \(y=−6\) are parallel. Two lines that have the same slope are called parallel lines. Find the \(x\)- and \(y\)-intercepts, a third point, and then graph. & {y}&{=m x+b} &{y}&{=}&{m x+b} \\{} & {m_{1}} & {=-\frac{7}{2} }&{ m_{2}}&{=}&{-\frac{2}{7}}\end{array}\). Estimate the temperature when there are no chirps. If you recognize right away from the equations that these are horizontal lines, you know their slopes are both \(0\). Compare these values to the equation \(y=mx+b\). Find the Fahrenheit temperature for a Celsius temperature of \(20\). Level up on the above skills and collect up to 600 Mastery points Start quiz. The slope of curve ZZ at point A is: Refer to the above diagram. Refer to the above diagram. Here are six equations we graphed in this chapter, and the method we used to graph each of them. \(\begin{array}{llll}{\text{Write each equation in slope-intercept form.}} Slope. 3. B. is 50. The first equation is already in slope–intercept form: \(\quad y=−5x−4\) 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. Graph the line of the equation \(y=2x−3\) using its slope and \(y\)-intercept. Use slopes to determine if the lines, \(y=−5x−4\) and \(x−5y=5\) are perpendicular. The \(C\)-intercept means that when the number of miles driven is \(0\), the weekly cost is \($60\). \(x=a\) is a vertical line passing through the \(x\)-axis at \(a\). But we recognize them as equations of vertical lines. B)3 and -11/3 respectively. Since their \(x\)-intercepts are different, the vertical lines are parallel. Interpret the slope and \(h\)-intercept of the equation. Interpret the slope and \(F\)-intercept of the equation. The red lines show us the rise is \(1\) and the run is \(2\). Use the following to answer questions 30-32: 30. \(y=\frac{2}{5}x−1\) D)cannot be determined from the information given. So I would rule that one out. Use slopes and \(y\)-intercepts to determine if the lines \(2x+5y=5\) and \(y=−\frac{2}{5}x−4\) are parallel. 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. In the above diagram variables x and y are: A. both dependent variables. The lines have the same slope, but they also have the same \(y\)-intercepts. Identify the slope and \(y\)-intercept of the line with equation \(x+2y=6\). We’ll use the points \((0,1)\) and \((1,3)\). By the end of this section, you will be able to: Before you get started, take this readiness quiz. In Graph Linear Equations in Two Variables, we graphed the line of the equation \(y=12x+3\) by plotting points. If the equation is of the form \(Ax+By=C\), find the intercepts. Find the slope-intercept form of the equation of the line. The slopes are negative reciprocals of each other, so the lines are perpendicular. Show transcribed image text. Find the Fahrenheit temperature for a Celsius temperature of \(0\). 5. Identify the slope and \(y\)-intercept of the line \(y=−\frac{4}{3}x+1\). &{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.}} Step 1: Begin by plotting the y-intercept of the given equation which is \left( {0,3} \right). The slope of curve ZZ at point B is: Refer to the above diagram. The vertical intercept: A. is 40. C) infinite. You may want to graph these lines, too, to see what they look like. It is for the material and labor needed to produce each item. After 4 miles, the elevation is 6200 feet above sea level. B. the intercept only. Perpendicular lines are lines in the same plane that form a right angle. Starting at the \(y\)-intercept, count out the rise and run to mark the second point. The break-even level of disposable income: A) is zero. We saw better methods in sections 4.3, 4.4, and earlier in this section. 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. Write the slope–intercept form of the equation of the line. A true water table seldom is encountered until well down the valley Use slopes to determine if the lines \(5x+4y=1\) and \(4x+5y=3\) are perpendicular. 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. C) both the slope and the intercept. &{ 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}\). The slope, \(\frac{1}{4}\), means that the temperature Fahrenheit (\(F\)) increases \(1\) degree when the number of chirps, \(n\), increases by \(4\). The slopes are reciprocals of each other, but they have the same sign. Since f(0) = -7.2(0) + 250 = 250, the vertical intercept is 250. The first equation is already in slope–intercept form: \(y=−2x+3\). Graph the equation. \(y=−6\) \(5x−3y=15\) if the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis). Interpret the slope and \(C\)-intercept of the equation. The second equation is now in slope-intercept form as well. The \(h\)-intercept means that when the shoe size is \(0\), the height is \(50\) inches. C. 3 and + 3 / 4 respectively. Count out the rise and run to mark the second point. The Keynesian cross diagram depicts the equilibrium level of national income in the G&S market model. 4 and -1 1/3 respectively. \[\begin{array}{lll}{\text{#1}}&{\text {Equation }} & {\text { Method }} \\ {\text{#2}}&{x=2} & {\text { Vertical line }} \\ {\text{#3}}&{y=4} & {\text { Hortical line }} \\ {\text{#4}}&{-x+2 y=6} & {\text { Intercepts }} \\ {\text{#5}}&{4 x-3 y=12} & {\text { Intercepts }} \\ {\text{#6}}&{y=4 x-2} & {\text { Slope-intercept }} \\{\text{#7}}& {y=-x+4} & {\text { Slope-intercept }}\end{array}\]. 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.”.

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