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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

Respuesta :

mhanifa

Answer:

  • 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
semsee45

Answer:

[tex]\boxed{y=500-60x}[/tex]

where:

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

Step-by-step 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:

[tex]\implies \textsf{Rate of change}=\dfrac{\textsf{change in $y$}}{\textsf{change in $x$}}=\dfrac{500-200}{0-5}=-60[/tex]

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:

[tex]\boxed{y=500-60x}[/tex]

where:

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

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