Question

Marco is driving to the grand canyon. his distance from the grand canyon decreases 150 miles every 3 hrs. After 4 hrs, his distance from the Grand Canyon is 200 miles. Marco's distance from the Grand Canyon in miles, y, is a function of the number of hours he drives, x. Find the initial value.

Answer 1

The initial value is 400.

The situation is described by a linear function of the form
`y=mx+b` where:

m = slope/rate of change

b = initial value

In this case, the distance y is decreasing 150 miles every 3 hours. So the rate of change (m) is equal to:

-150/3 = -50 miles per hour

Now we know that after 4 hours, his distance is 200 miles. We can plug in x = 4 and y = 200 into the linear equation.

200 = -50(4) + b

200 = -200 + b

400 = b