Graphing Linear Equations in Slope-Intercept Form
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1 4.4. Graphing Linear Equations in Slope-Intercept Form equation = m + b? How can ou describe the graph of the ACTIVITY: Analzing Graphs of Lines Work with a partner. Graph each equation. Find the slope of each line. Find the point where each line crosses the -ais. Complete the table. Equation a. = + b. = + Slope of Graph Point of Intersection with -ais c. = d. = + e. = + f. = COMMON CORE Graphing Equations In this lesson, ou will find slopes and -intercepts of graphs of linear equations. graph linear equations written in slope-intercept form. Learning Standard 8.EE.6 g. = h. = i. = + j. = k. Do ou notice an relationship between the slope of the graph and its equation? between the point of intersection with the -ais and its equation? Compare the results with those of other students in our class. 66 Chapter 4 Graphing and Writing Linear Equations
2 ACTIVITY: Deriving an Equation Work with a partner. a. Look at the graph of each equation in Activit. Do an of the graphs represent a proportional relationship? Eplain. b. For a nonproportional linear relationship, the graph crosses the -ais at some point (0, b), where b does not equal 0. Let (, ) represent an other point on the graph. You can use the formula for slope to write the equation for a nonproportional linear relationship. Use the graph to complete the steps. (0, b) (, ) = m Slope formula = m Substitute values. Math Practice Use Prior Results How can ou use the results of Activit to help support our answer? = m Simplif. = m Multiplication Propert of Equalit = m Simplif. = m + Addition Propert of Equalit c. What do m and b represent in the equation?. IN YOUR OWN WORDS How can ou describe the graph of the equation = m + b? a. How does the value of m affect the graph of the equation? b. How does the value of b affect the graph of the equation? c. Check our answers to parts (a) and (b) with three equations that are not in Activit. 4. LOGIC Wh do ou think = m + b is called the slope-intercept form of the equation of a line? Use drawings or diagrams to support our answer. Use what ou learned about graphing linear equations in slope-intercept form to complete Eercises 4 6 on page 70. Section 4.4 Graphing Linear Equations in Slope-Intercept Form 67
3 4.4 Lesson Lesson Tutorials Ke Vocabular -intercept, p. 68 -intercept, p. 68 slope-intercept form, p. 68 Intercepts The -intercept of a line is the -coordinate of the point where the line crosses the -ais. It occurs when = 0. (0, b) -intercept b -intercept a The -intercept of a line is the -coordinate of the point where the line crosses the -ais. It occurs when = 0. O (a, 0) Stud Tip Linear equations can, but do not alwas, pass through the origin. So, proportional relationships are a special tpe of linear equation in which b = 0. Slope-Intercept Form Words A linear equation written in the form = m + b is in slope-intercept form. The slope of the line is m, and the -intercept of the line is b. Algebra = m + b slope -intercept EXAMPLE Identifing Slopes and -Intercepts Find the slope and the -intercept of the graph of each linear equation. a. = 4 = 4 + ( ) Write in slope-intercept form. The slope is 4, and the -intercept is. b. 5 = = + 5 Add 5 to each side. The slope is, and the -intercept is 5. Find the slope and the -intercept of the graph of the linear equation. Eercises 7 5. = 7. = 68 Chapter 4 Graphing and Writing Linear Equations
4 EXAMPLE Graphing a Linear Equation in Slope-Intercept Form Graph = +. Identif the -intercept. Step : Find the slope and the -intercept. = + slope -intercept Check 4 Step : The -intercept is. So, plot (0, ). Step : Use the slope to find another point and draw the line. m = rise run = Plot the point that is unit right and units down from (0, ). Draw a line through the two points. (0, ) The line crosses the -ais at (, 0). So, the -intercept is. EXAMPLE Real-Life Application The cost (in dollars) of taking a tai miles is =.5 +. (a) Graph the equation. (b) Interpret the -intercept and the slope. a. The slope of the line is.5 = 5. Use the slope and the -intercept to graph the equation. The -intercept is. So, plot (0, ) (0, ) 5 Use the slope to plot another point, (, 7). Draw a line through the points b. The slope is.5. So, the cost per mile is $.50. The -intercept is. So, there is an initial fee of $ to take the tai. Eercises 8 Graph the linear equation. Identif the -intercept. Use a graphing calculator to check our answer.. = 4 4. = + 5. In Eample, the cost (in dollars) of taking a different tai miles is = +.5. Interpret the -intercept and the slope. Section 4.4 Graphing Linear Equations in Slope-Intercept Form 69
5 4.4 Eercises Help with Homework. VOCABULARY How can ou find the -intercept of the graph of + = 6?. CRITICAL THINKING Is the equation = in slope-intercept form? Eplain.. OPEN-ENDED Describe a real-life situation that ou can model with a linear equation. Write the equation. Interpret the -intercept and the slope. 9+(-6)= +(-)= 4+(-9)= 9+(-)= Match the equation with its graph. Identif the slope and the -intercept. 4. = + 5. = 6. = + A. B. C. Find the slope and the -intercept of the graph of the linear equation. 7. = = = = = 4. 6 = 8..5 = 4. = 5 5. = ERROR ANALYSIS Describe and correct the error in finding the slope and the -intercept of the graph of the linear equation. = 4 The slope is 4, and the -intercept is. 7. SKYDIVING A skdiver parachutes to the ground. The height (in feet) of the skdiver after seconds is = a. Graph the equation. b. Interpret the -intercept and the slope. 70 Chapter 4 Graphing and Writing Linear Equations
6 Graph the linear equation. Identif the -intercept. Use a graphing calculator to check our answer. 8. = = = = =. = APPLES You go to a harvest festival and pick apples. a. Which equation represents the cost (in dollars) of going to the festival and picking pounds of apples? Eplain. = = b. Graph the equation ou chose in part (a). 5. REASONING Without graphing, identif the equations of the lines that are (a) parallel and (b) perpendicular. Eplain our reasoning. = + 4 = = = + = + = + = + 5 = 6. Si friends create a website. The website earns mone b selling banner ads. The site has 5 banner ads. It costs $0 a month to operate the website. a. A banner ad earns $0.005 per click. Write a linear equation that represents the monthl income (in dollars) for clicks. b. Graph the equation in part (a). On the graph, label the number of clicks needed for the friends to start making a profit. Solve the equation for. (Section.4) 7. = = 9. = = 8. MULTIPLE CHOICE Which point is a solution of the equation 8 =? (Section 4.) A (, ) B (, ) C (, ) D (, ) Section 4.4 Graphing Linear Equations in Slope-Intercept Form 7
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