Question

Question 2 of 15

A car travels along the highway to Austin at a steady speed. When it begins, it
is 500 miles from Austin. After 5 hours, it is 200 miles from Austin. Which
function describes the car's distance from Austin? Helpppp

Answer 1

`\boxed{y=500-60x}`

where:

• x is the time (in hours).
• y is the car's distance from Austin (in miles).

Explanation:

Define the variables:

• Let x be the time (in hours).
• Let y be the car's distance from Austin (in miles).

Given:

• When x = 0, y = 500.
• When x = 5, y = 200.

Find the rate of change:

`\implies \textsf{Rate of change}=\frac{\textsf{change in $y$}}{\textsf{change in $x$}}=(500-200)/(0-5)=-60`

Therefore, for every hour that passes, the car is 60 miles closer to Austin.

Therefore, the function that describes the car's distance from Austin is:

`\boxed{y=500-60x}`

where:

• x is the time (in hours).
• y is the car's distance from Austin (in miles).

Answer 2

• d(h) = 500 - 60h

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This relationship is linear

• Initial value is 500,
• The rate of change (speed) is (200 - 500)/5 = - 300/5 = - 60

The function to reflect this situation is

• d(h) = 500 - 60h, where d- distance from Austin, h - number of hours in travel