Calculus Volume 1

Chapter 1 | Functions and Graphs

39

Figure 1.17 Finding the equation of a linear function with a graph that is a line between two given points.

a. Find the slope of the line. b. Find an equation for this linear function in point-slope form. c. Find an equation for this linear function in slope-intercept form.

Solution

a. The slope of the line is

y 2 − y 1 x 2 − x 1

9 15

m = . b. To find an equation for the linear function in point-slope form, use the slope m =−3/5 and choose any point on the line. If we choose the point (11, −4), we get the equation f ( x )+4= − 3 5 ( x −11). c. To find an equation for the linear function in slope-intercept form, solve the equation in part b. for f ( x ). When we do this, we get the equation f ( x ) = − 3 5 x + 13 5 . = 5−(−4) −4−11 = − = − 3 5

1.9 Consider the line passing through points (−3, 2) and (1, 4). Find the slope of the line. Find an equation of that line in point-slope form. Find an equation of that line in slope-intercept form.

Example 1.13 A Linear Distance Function

Jessica leaves her house at 5:50 a.m. and goes for a 9-mile run. She returns to her house at 7:08 a.m. Answer the following questions, assuming Jessica runs at a constant pace.

Made with FlippingBook - professional solution for displaying marketing and sales documents online