Slope. SAFETY A ladder truck uses a moveable ladder to reach upper levels of houses and buildings.

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1 9- MAIN IDEA Find the slope of a line. New Vocabular Slope SAFETY A ladder truck uses a moveable ladder to reach upper levels of houses and buildings. 1. The rate of change of the slope Math nline glencoe.com Etra Eamples Personal Tutor Self-Check Quiz ladder compares the height it is raised to the distance of its base from the building. Write this rate as a fraction in simplest form. ft 2. Find the rate of change of a 0 ft ladder that has been raised 100 feet and has a base of 0 feet from the building. The term slope is used to describe how steep a straight line is numericall. Slope is the ratio of the, or vertical change, to the, or horizontal change. In linear functions, no matter which two points ou choose, the slope, or rate of change, of the line is alwas constant. slope = _ vertical change between an two points horizontal change between the same two points 1 EXERCISE Find the slope of the treadmill at the right. slope = _ 10 in. =_ 8 in. =_ 2 Definition of slope = 10 in., = 8 in. 10 in. 8 in. Simplif. The slope of the treadmill is _. 2 a. HIKING A hiking trail s 6 feet for ever horizontal change of 100 feet. What is the slope of the hiking trail? Since slope is a rate of change, it can be positive (slanting upward) or negative (slanting downward). Lesson 9- Slope 81_86_C09_L0_8700.indd /20/07 10:00: AM

2 Find Slope Using a Graph Translating Rise and Run up positive down negative right positive left negative 2 Find the slope of the line. Choose two points on the line. The vertical change is 2 units while the horizontal change is units. slope = _ Definition of slope = _ 2 = 2, = The slope of the line is _ 2. 2 b. c. Slope can be found b finding the ratio of the change in -values () to the change in -values () for an two points on a line. Find Slope Using a Table Slope You can choose an two points to calculate slope. Whichever -value ou use first, be sure to use the corresponding -value first. The points given in the table lie on a line. Find the slope of the line. Then graph the line. Choose two points from the table to find the changes in the - and -values. change in slope = _ change in = _ = _ - 2 or - _ 2 The slope is - _ (1, 12) - 2 (, 9) (, 6) (7, ) d e Chapter 9 Algebra: Linear Functions 81_86_C09_L0_8700.indd 82 9/20/07 10:00:7 AM

3 Reading Math Subscripts 1 is read sub one and 2 is read sub two. The are used to indicate two different -coordinates. You have found slope b using _ change in and _. You can also find change in the slope of a line b using the coordinates of an two points on the line. ne point can be represented b ( 1, 1 ) and the other b ( 2, 2 ). The small numbers slightl below and are called subscripts. Slope Formula Ke Concept Words The slope m of a line passing through points ( 1, 1 ) and ( 2, 2 ) is the ratio of the difference in the -coordinates to the corresponding difference in the -coordinates. Model ( 1, 1 ) ( 2, 2 ) Smbols m = _ , where Find Slope Using Coordinates Find the slope of the line that passes through each pair of points. C(-1, -), D(2, 2) m = _ Slope formula 1 m = _ 2 - (-) 2 - (-1) ( 1, 1 ) = (-1, -) ( 2, 2 ) = (2, 2) m = _ 6 or 2 Simplif. Check When going from left to right, the graph of the line slants upward. This is correct for positive slope. (-1, -) (2, 2) Using the Slope Formula It does not matter which point ou define as ( 1, 1 ) and ( 2, 2 ). However, the coordinates of both points must be used in the same order. To check Eample, let ( 1, 1 ) = (-, ) and ( 2, 2 ) = (1, 2). Then find the slope. R(1, 2), S(-, ) m = _ m = _ m = 1_ - or - 1_ Slope formula ( 1, 1 ) = (1, 2) ( 2, 2 ) = (-, ) Simplif. Check When going from left to right, the graph of the line slants downward. This is correct for negative slope. (-, ) (1, 2) f. A(2, 2), B(, ) g. C(-2, 1), D(0, -) h. J(-7, -), K(-, -2) Lesson 9- Slope 8 81_86_C09_L0_8700.indd 8 9/20/07 10:00:9 AM

4 Eample 1 (p. 81) 1. BUILDINGS Find the slope of the roof of the storage shed. ft 1 ft Eample 2 (p. 82) Find the slope of each line. 2.. Eample (p. 82) Eamples, (p. 8). The points given in the table lie on a line. Find the slope of the line. Then graph the line. 1 7 Find the slope of the line that passes through each pair of points.. A(-, -2), B(, ) 6. C(-, 2), D(1, ) 7. E(-6, ), F(, -) 8. G(1, ), H(, -) For Eercises See Eamples 9, , , HELP HMEWRK HELP 9. SKIING Find the slope of a ski 10. RADS Find the slope of a road that descends 1 feet for that s 12 feet for ever ever horizontal change of 2 feet. horizontal change of 100 feet. 1 ft 100 ft 12 ft 2 ft Find the slope of each line Chapter 9 Algebra: Linear Functions 81_86_C09_L0_8700.indd 8 9/20/07 10:00:1 AM

5 The points given in each table lie on a line. Find the slope of the line. Then graph the line Find the slope of the line that passes through each pair of points. 17. A(0, 1), B(2, 7) 18. C(2, ), D(, 1) 19. E(1, 2), F(, 7) 20. G(-6, -1), H(, 1) 21. J(-9, ), K(2, 1) 22. M(-2, ), N(7, -) 2. AQUARIUMS The graph shows the depth of water in an aquarium over several das. Find the slope of the line and eplain its meaning as a rate of change. JBS For Eercises 2 26, use the following information. For working hours, Sofia earns $0.60. For working hours, she earns $1. For working 6 hours, she earns $ Depth (in.) Water in Aquarium Da 2. Graph the information with the hours on the horizontal ais and mone earned on the vertical ais. Draw a line through the points. 2. What is the slope of the graph? 26. What does the slope of the graph represent? HUSING For Eercises 27 29, use the U.S. Home wnership graph at the right. 27. Find the slope of the line representing the change between each three-ear 67 period Does the graph show a constant rate 6 of change? Eplain If the graph is etended in each direction, could ou epect the slope to remain constant throughout the graph? Eplain. Source: U.S. Census Bureau C11-29A-8700.ai 0. GEMETRY Two lines that are parallel have the same slope. Determine whether quadrilateral ABCD is a parallelogram. Justif our reasoning. Percent of Families Year PRACTICE EXTRA PRACTICE See pages 692, DISABILITIES Wheelchair ramps for access to public buildings are allowed a maimum of one inch of vertical increase for ever one foot of horizontal distance. Would a ramp that is 10 feet long and 8 inches tall meet this guideline? Eplain our reasoning. Lesson 9- Slope 8 81_86_C09_L0_8700.indd Gr8 MS Math SE /10/09 11:: AM

6 2. PEN ENDED Write the coordinates of two points. Show that ou can define H..T. Problems either point as ( 1, 1) and the slope of the line containing the points will be the same.. FIND THE ERRR Jabali and Joel are finding the slope of the line that passes through X(0, 2) and Y(2, ). Who is correct? Eplain. -2 m=_ _1 m=_ -2 or m=_ 2-0 m = _21 Jabali Joel. CHALLENGE Find the slope of the straight line that is the graph of the function epressing the circumference of a circle as a function of the radius.. WR ITING IN MATH For the slope of a linear function, eplain wh the vertical change () and the horizontal change () is alwas the same. 6. Which line graphed below has a slope 7. What is the slope of the linear function of -2? A shown in the graph? C B D H _ F -_ G -_ C11-0C-8296-AC11-07C-8296-A J _ C09-2A ai C11-06C-8296-A C11-08C-8296-A Graph each function. (Lesson 9-) 8. = 9. = = = TEMPERATURE The function used to change a Celsius temperature C to 9 C + 2. Change 2 Celsius to a Fahrenheit temperature F is F = _ Fahrenheit. (Lesson 9-2) PREREQUISITE SKILL Solve each equation.. 2 = = 18a (Lesson 1-10). n _ = = _ t 9 Chapter 9 Algebra: Linear Functions 81_86_C09_L0_8700.indd 86 7/10/09 11:0:8 AM