Ryan is driving to Phoenix. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Ryan has 58 miles to his destination after 33 minutes of driving, and he has 46.8 miles to his destination after 47 minutes of driving. How many miles will he have to his destination after 51 minutes of driving?

he have 43.6 miles to his destination after 51 minutes of driving.

Step-by-step explanation:

let x represent his total driving time (in minutes).

Let y represent the number of miles that Ryan has to his destination.

If we plot y on the vertical axis and x on the horizontal axis, a straight line would be formed. The slope of the straight line would be

Slope, m = (58 - 46.8)/(33 - 47)

m = 11.2/- 14 = - 0.8

The equation of the straight line can be represented in the slope-intercept form, y = mx + c

Where

c = intercept

m = slope

To determine the intercept, we would substitute x = 33, y = 58 and m = - 0.8 into y = mx + c. It becomes

58 = - 0.8 × 33 + c

58 = - 26.4 + c

c = 58 + 26.4

c = 84.4

The linear function becomes

y = - 0.8x + 84.4

Therefore, after 51 minutes, the number of miles that he has to his destination is

y = - 0.8 × 51 + 84.4

y = 43.6

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