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CHAPTER 3 Graphs of Liner Equations Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 3.1Graphs and Applications of Linear Equations 3.2More with Graphing and Intercepts 3.3Slope and Applications 3.4Equations of Lines 3.5Graphing Using the Slope and the y-Intercept 3.6Parallel and Perpendicular Lines 3.7Graphing Inequalities in Two Variables

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OBJECTIVES 3.3 Slope and Applications Slide 3Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. aGiven the coordinates of two points on a line, find the slope of the line, if it exists. bFind the slope of a line from an equation. cFind the slope, or rate of change, in an applied problem involving slope.

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We have looked at two forms of a linear equation, Ax + By = C and y = mx + b We know that the y-intercept of a line is (0, b). y = mx + b ? The y-intercept is (0, b). What about the constant m? Does it give certain information about the line? 3.3 Slope and Applications a Given the coordinates of two points on a line, find the slope of the line, if it exists. Slide 4Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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Look at the following graphs and see if you can make any connections between the constant m and the “slant” of the line. y x y x y x y x 3.3 Slope and Applications a Given the coordinates of two points on a line, find the slope of the line, if it exists. Slide 5Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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The slope of the line containing points (x 1, y 1 ) and (x 2, y 2 ) is given by 3.3 Slope and Applications Slope Slide 6Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution 3.3 Slope and Applications a Given the coordinates of two points on a line, find the slope of the line, if it exists. A Graph the line containing the points ( 4, 5) and (4, 1) and find the slope. (continued) Slide 7Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution rise run 3.3 Slope and Applications a Given the coordinates of two points on a line, find the slope of the line, if it exists. A Graph the line containing the points ( 4, 5) and (4, 1) and find the slope. Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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The slope of a line tells how it slants. A line with a positive slope slants up from left to right. The larger the slope, the steeper the slant. A line with a negative slope slants downward from left to right. 3.3 Slope and Applications a Given the coordinates of two points on a line, find the slope of the line, if it exists. Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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The slope of the line y = mx + b is m. To find the slope of a nonvertical line, solve the linear equation in x and y for y and get the resulting equation in the form y = mx + b. The coefficient of the x-term, m is the slope of the line. It is possible to find the slope of a line from its equation. 3.3 Slope and Applications Determining Slope from the Equation y = mx + b Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE m = 1 = Slope a.b. c. y = x + 8 d. m = 4 = Slope m = = Slope m = 0.25 = Slope 3.3 Slope and Applications b Find the slope of a line from an equation. BFind the slope of the line. Slide 11Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE We solve for y to get the equation in the form y = mx + b. 3x + 5y = 15 5y = –3x + 15 The slope is 3.3 Slope and Applications b Find the slope of a line from an equation. CFind the slope of the line 3x + 5y = 15. Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution Consider the points ( 3, 3) and (2, 3), which are on the line. A horizontal line has slope 0. ( 3, 3) (2, 3) 3.3 Slope and Applications b Find the slope of a line from an equation. DFind the slope of the line y = 3. Slide 13Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution Consider the points (2, 4) and (2, 2), which are on the line. The slope of a vertical line is undefined. (2, 4) (2, 2) 3.3 Slope and Applications b Find the slope of a line from an equation. EFind the slope of the line x = 2. Slide 14Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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The slope of a horizontal line is 0. The slope of a vertical line is not defined. 3.3 Slope and Applications Slope 0; Slope Not Defined Slide 15Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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Applications of Slope Some applications use slope to measure the steepness. For examples, numbers like 2%, 3%, and 6% are often used to represent the grade of a road, a measure of a road’s steepness. That is, a 3% grade means that for every horizontal distance of 100 ft, the road rises or drops 3 ft. 3.3 Slope and Applications c Find the slope, or rate of change, in an applied problem involving slope. Slide 16Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE 0.42 ft 5.5 ft The grade of the treadmill is 7.6%. ** Reminder: Grade is slope expressed as a percent. Solution 3.3 Slope and Applications c Find the slope, or rate of change, in an applied problem involving slope. FFind the slope (or grade) of the treadmill. Slide 17Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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