Exercise 36 Page 180

Practice makes perfect

a Let's recall the slope-intercept form of a linear function.

y= mx+ b In this formula m indicates the slope and b indicates the y-intercept. If we look at the graph, it appears as though the function passes through two ordered pairs comprised of integer values, (0,8) and (9,10).

Graph of U.S. box office revenues from 2000 to 2012.

Let's use these points to find the slope using the Slope Formula.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 0,8) & ( 9,10)

m=10- 8/9- 0

SubTerms

Subtract terms

m=2/9

The y-intercept is the value of y when the function crosses the y-axis. In this case we have b= 8, which we know from the points we identified earlier. Let's summarize what we have found. Slope:& m=2/9 y-intercept:& b=8

b To understand the previous results we need to put them in the context of the x- and y-axis labels. We are told that the x-axis represents the number of years since 2000 and the y-axis represents the revenues of the U.S. Box Office in billions of dollars. Let's recall the answers from Part A.

Slope:& m= 2/9 y-intercept:& b= 8 The slope tells us that the revenue increases by 29≈ 0.22 billion dollars per year. The y-intercept tells us that the revenue in the year 2000 was 8 billion dollars.

c Having found the slope and y-intercept, we can easily write an equation for this function in slope-intercept form.

y= mx+ b ⇒ y= 2/9x+ 8 Now, since we know that the x-axis represents years since 2000 we can predict the revenue in 2018 by substituting 18 for x.

y=1/5x+8

Substitute

x= 18

y=1/5( 18)+8

▼

Evaluate right-hand side

MoveRightFacToNumOne

1/b* a = a/b

y=18/5+8

CalcQuot