Slope and Applications One form of linear equations we have examined is y = mx + b –The y-intercept is at (0,b) –The constant m represents the slope of the graph The slope = m = rise / run = change in y / change in x = (y 2 - y 1 ) / (x 2 - x 1 ) rise run (3,2) (6,4) (-2,4) (1,-2) rise run Graph the lines connecting the following points and find the slopes… –(3,2) and (6,4) Slope = –(-2,4) and (1,-2) Slope =

Applications of Slope The slope of a graph and how it slants are related as follows –Slants up left to right => Positive slope (positive change in y, positive change in x) –Slants downward from left to right => Negative slope (negative change in y, positive change in x) –Horizontal => 0 slope (change in y is 0) –Vertical => Undefined slope (change in x is 0) Example: –Suppose a road rises 40 ft. over a horizontal distance of 281 ft. Sketch the problem, approximate the slope of the road / grade of the hill.

Applications of Slope Slope can also be considered as a rate of change Examples: –The following graph shows data for Oscar the Grouch’s Minican driven on interstate highways. Find the rate of change (miles per gallon) Gasoline Consumed (gallons) Number miles driven Find the change in y over the change in x from 2 representative points

Slope from Equations Slope can easily be found in equations by examining the slope- intercept form (slope = m in y = mx + b) Examples: –Find the slopes of the lines in… y = -2x y = 3x + 4 y = ½ x – 3 y = 7 4x + 2y = -8 x = -2 3x - 9y = 18 Additional HW: 1, 2, 5, 7, 13, 16, 26, 37, 41, 45, 55, 56