. Slope of a Line describe the line? How can ou use the slope of a line to Slope is the rate of change between an two points on a line. It is the measure of the steepness of the line. To find the slope of a line, find the ratio of the change in (vertical change) to the change in (horizontal change). change in slope = change in 7 Slope 7 ACTIVITY: Finding the Slope of a Line Work with a partner. Find the slope of each line using two methods. Method : Use the two black points. Method : Use the two pink points. Do ou get the same slope using each method? Wh do ou think this happens? a. b. Graphing Equations In this lesson, ou will find slopes of lines b using two points. find slopes of lines from tables. c. d. 7 Chapter Graphing and Writing Linear Equations
ACTIVITY: Using Similar Triangles Work with a partner. Use the figure shown. a. ABC is a right triangle formed b drawing a horizontal line segment from point A and a vertical line segment from point B. Use this method to draw another right triangle, DEF. b. What can ou conclude about ABC and DEF? Justif our conclusion. c. For each triangle, find the ratio of the length of the vertical side to the length of the horizontal side. What do these ratios represent? d. What can ou conclude about the slope between an two points on the line? 0 9 8 7 A(, ) B(, ) D(9, ) C(, ) E(, 0) 7 8 9 0 ACTIVITY: Drawing Lines with Given Slopes Math Practice Interpret a Solution What does the slope tell ou about the graph of the line? Eplain. Work with a partner. a. Draw two lines with slope. ne line passes through (, ), and the other line passes through (, 0). What do ou notice about the two lines? b. Draw two lines with slope. ne line passes through (, ), and the other line passes through (, ). What do ou notice about the two lines? c. CNJECTURE Make a conjecture about two different nonvertical lines in the same plane that have the same slope. d. Graph one line from part (a) and one line from part (b) in the same coordinate plane. Describe the angle formed b the two lines. What do ou notice about the product of the slopes of the two lines? e. REPEATED REASNING Repeat part (d) for the two lines ou did not choose. Based on our results, make a conjecture about two lines in the same plane whose slopes have a product of.. IN YUR WN WRDS How can ou use the slope of a line to describe the line? Use what ou learned about the slope of a line to complete Eercises on page 77. Section. Slope of a Line 7
. Lesson Lesson Tutorials Ke Vocabular slope, p. 7 rise, p. 7 run, p. 7 Reading In the slope formula, is read as sub one, and is read as sub two. The numbers and in and are called subscripts. Slope The slope m of a line is a ratio of the change in (the rise) to the change in (the run) between an two points, (, ) and (, ), on the line. m = rise run change in = change in = Positive Slope The line rises from left to right. (, ) (, ) Rise Run Negative Slope The line falls from left to right. EXAMPLE Finding the Slope of a Line Describe the slope of the line. Then find the slope. a. (, ) (, ) b. (, ) (, ) Stud Tip When finding slope, ou can label either point as (, ) and the other point as (, ). The line rises from left to The line falls from left to right. So, the slope is positive. right. So, the slope is negative. Let (, ) = (, ) and Let (, ) = (, ) and (, ) = (, ). (, ) = (, ). m = m = ( ) = ( ) = = ( ) =, or 7 Chapter Graphing and Writing Linear Equations
Eercises 7 9 Find the slope of the line.. (, ) (, ). (, ) (, ). (, ) (, ) EXAMPLE Finding the Slope of a Horizontal Line Find the slope of the line. m = = ( ) (, ) (, ) = 0 7, or 0 The slope is 0. Stud Tip EXAMPLE The slope of ever horizontal line is 0. The slope of ever vertical line is undefined. Finding the Slope of a Vertical Line Find the slope of the line. m = = = 0 (, ) (, ) Because division b zero is undefined, the slope of the line is undefined. Eercises Find the slope of the line through the given points.. (, ), (7, ). (, ), (, ). (, ), (, ) 7. (0, 8), (0, 0) 8. How do ou know that the slope of ever horizontal line is 0? How do ou know that the slope of ever vertical line is undefined? Section. Slope of a Line 7
EXAMPLE Finding Slope from a Table The points in the table lie on a line. How can ou find the slope of the line from the table? What is the slope? 7 0 8 Choose an two points from the table and use the slope formula. Use the points (, ) = (, 8) and (, ) = (, ). m = = 8 =, or The slope is. Check 8 7 (, 8) (, ) (7, ) (0, ) 7 8 9 0 Eercises The points in the table lie on a line. Find the slope of the line. 9. 0. 7 0 8 0 Slope Positive Slope Negative Slope Slope of 0 Undefined Slope The line rises The line falls The line is The line is from left to right. from left to right. horizontal. vertical. 7 Chapter Graphing and Writing Linear Equations
. Eercises Help with Homework. CRITICAL THINKING Refer to the graph. a. Which lines have positive slopes? b. Which line has the steepest slope? c. Do an lines have an undefined slope? Eplain.. PEN-ENDED Describe a real-life situation in which ou need to know the slope. A B C. REASNING The slope of a line is 0. What do ou know about the line? 9+(-)= +(-)= +(-9)= 9+(-)= Draw a line through each point using the given slope. What do ou notice about the two lines?. slope =. slope =. slope = Find the slope of the line. 7. (, 0) (, ) 8. (, ) (, 0) 9. (, ) (, ) 0. (, ) (, ). (, ) (, ). (, ) (, ) Section. Slope of a Line 77
Find the slope of the line through the given points.. (, ), (, ). (, ), (, 8). ( 7, 0), ( 7, ). (, ), (, ) 7. (0, ), (, ) 8. (, ), (, ) 9. ERRR ANALYSIS Describe and correct the error in finding the slope of the line. 0. CRITICAL THINKING Is it more difficult to walk up the ramp or the hill? Eplain. m = = = (, ) (, ) ft hill ramp 8 ft 8 ft ft The points in the table lie on a line. Find the slope of the line.. 7. 7 0 8 0.. 8 0 8 8 ft ft. PITCH Carpenters refer to the slope of a roof as the pitch of the roof. Find the pitch of the roof.. PRJECT The guidelines for a wheelchair ramp suggest that the ratio of the rise to the run be no greater than :. a. CHSE TLS Find a wheelchair ramp in our school or neighborhood. Measure its slope. Does the ramp follow the guidelines? b. Design a wheelchair ramp that provides access to a building with a front door that is. feet above the sidewalk. Illustrate our design. Use an equation to find the value of k so that the line that passes through the given points has the given slope. 7. (, ), (, k); m = 8. (, k), (, 0); m = 9. (, k), (, 7); m = 0. (, ), (k, ); m = 78 Chapter Graphing and Writing Linear Equations
. TURNPIKE TRAVEL The graph shows the cost of traveling b car on a turnpike. a. Find the slope of the line. b. Eplain the meaning of the slope as a rate of change. Cost (dollars).0.0 Turnpike Travel. BAT RAMP Which is steeper: the boat ramp or a road with a % grade? Eplain. (Note: Road grade is the vertical increase divided b the horizontal distance.) 0 0 8 Miles driven ft ft. REASNING Do the points A(, ), B(, ), and C(, ) lie on the same line? Without using a graph, how do ou know?. BUSINESS A small business earns a profit of $00 in Januar and $7,00 in Ma. What is the rate of change in profit for this time period?. STRUCTURE Choose two points in the coordinate plane. Use the slope formula to find the slope of the line that passes through the two points. Then find the slope using the formula. Eplain wh our results are the same.. The top and the bottom of the slide are level with the ground, which has a slope of 0. ft a. What is the slope of the main portion of the slide? b. How does the slope change when the bottom of the slide is onl inches above the ground? Is the slide steeper? Eplain. ft 8 in. ft 8 ft Solve the proportion. (Section.) 7. b 0 = 8. 7 = n 9. 8 = 0 0. MULTIPLE CHICE What is the prime factorization of 8? (Skills Review Handbook) A 7 B 7 C 7 D Section. Slope of a Line 79