CHAPTER 11 Graphs of Linear Equations Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 11.1Graphs and Applications of Linear Equations 11.2More with Graphing and Intercepts 11.3Slope and Applications 11.4Equations of Lines 11.5Graphing Using the Slope and the y-Intercept 11.6Parallel and Perpendicular Lines 11.7Graphing Inequalities in Two Variables

OBJECTIVES 11.3 Slope and Applications Slide 3Copyright 2012, 2008, 2004, 2000 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.

11.3 Slope and Applications SLOPE Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

11.3 Slope and Applications a Given the coordinates of two points on a line, find the slope of the line, if it exists. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. In the preceding definition, (x 1, y 1 ) and (x 2, y 2 ) —read “x sub-one, y sub-one and x sub-two, y sub-two”—represent two different points on a line. It does not matter which point is considered (x 1, y 1 ) and which is considered (x 2, y 2 ) so long as coordinates are subtracted in the same order in both the numerator and the denominator.

EXAMPLE 11.3 Slope and Applications a Given the coordinates of two points on a line, find the slope of the line, if it exists. 1 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Graph the line containing the points (–4, 3) and (2, –6) and find the slope.

EXAMPLE 11.3 Slope and Applications a Given the coordinates of two points on a line, find the slope of the line, if it exists. 1 Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

11.3 Slope and Applications a Given the coordinates of two points on a line, find the slope of the line, if it exists. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The slope of a line tells how it slants. A line with positive slope slants up from left to right. The larger the slope, the steeper the slant. A line with negative slope slants downward from left to right.

11.3 Slope and Applications DETERMINING SLOPE FROM THE EQUATION y = mx + b Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 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.

EXAMPLE 11.3 Slope and Applications b Find the slope of a line from an equation. 2 Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Find the slope of each line.

EXAMPLE 11.3 Slope and Applications b Find the slope of a line from an equation. 6 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 11.3 Slope and Applications b Find the slope of a line from an equation. 7 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We can think of y = 5 as y = 0x + 5. Then from this equation, we see that m = 0. Any two points on a horizontal line have the same y-coordinate. The change in y is 0. Thus the slope of a horizontal line is 0.

EXAMPLE 11.3 Slope and Applications b Find the slope of a line from an equation. 8 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Consider the points (–4, 3) and (–4, –2) which are on the line. Since division by 0 is not defined, the slope of this line is not defined.

11.3 Slope and Applications SLOPE 0; SLOPE NOT DEFINED Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The slope of a horizontal line is 0. The slope of a vertical line is not defined.

EXAMPLE 11.3 Slope and Applications c Find the slope, or rate of change, in an applied problem involving slope. 9Skiing Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Among the steepest skiable terrain in North America, the Headwall on Mt. Washington, in New Hampshire, drops 720 ft over a horizontal distance of 900 ft. Find the grade of the Headwall. The grade of the Headwall is its slope, expressed as a percent:

11.3 Slope and Applications c Find the slope, or rate of change, in an applied problem involving slope. Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slope can also be considered as a rate of change.

EXAMPLE 11.3 Slope and Applications c Find the slope, or rate of change, in an applied problem involving slope. 10Masonry Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Jacob, an experienced mason, prepared a graph displaying data from a recent day’s work. Use the graph to determine the slope, or the rate of change of the number of bricks he can lay with respect to time.

EXAMPLE 11.3 Slope and Applications c Find the slope, or rate of change, in an applied problem involving slope. 10Masonry Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 11.3 Slope and Applications c Find the slope, or rate of change, in an applied problem involving slope. 10Masonry Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The vertical axis of the graph shows the number of bricks he has laid and the horizontal axis shows the time, in units of one hour. We can describe the rate of change of the number of bricks laid with respect to time as

EXAMPLE 11.3 Slope and Applications c Find the slope, or rate of change, in an applied problem involving slope. 10Masonry Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. This value is the slope of the line. We see two ordered pairs on the graph––in this case, This tells us that in the 2 hr between 9:00 and 11:00, 380 – 190, or 190, bricks were laid. Thus,