. Lesson Lesson Tutorials Ke Vocabular slope, p. 0 rise, p. 0 run, p. 0 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. 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 0 Chapter Graphing and Writing Linear Equations
Eercises 7 9. (, ) (, ). (, ) (, ). (, ) (, ) Finding the Slope of a Horizontal Line m = ( ) (, ) (, ) = 0 7, or 0 The slope is 0. Stud Tip The slope of ever horizontal line is 0. The slope of ever vertical line is undefined. Finding the Slope of a Vertical 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
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. 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. 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 = 7. (, 0) (, ) 8. (, ) (, 0) 9. (, ) (, ) 0. (, ) (, ). (, ) (, ). (, ) (, ) Section. Slope of a Line
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.. 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 = Chapter Graphing and Writing Linear Equations
. TURNPIKE TRAVEL The graph shows the cost of traveling b car on a turnpike. a. 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 ft of the slide is onl inches above the ground? Is the slide steeper? Eplain. 8 in. ft 8 ft Solve the proportion. 7. b 0 = (Skills Review Handbook) 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