Question

Carlos was driving at a constant speed. After three hours he was three hundred miles from E-Town on the highway at the 6 hours he was full and 80 miles from town which fraction which function represents Carlos distance y from the town after X hours

Answer 1

`y = -(220)/(3)x + 520`

Explanation:

Given

`x = time`

`y = distance`

For the first 3 hours, we have:

`(x_1,y_1) = (3,300)`

At 6 hours, we have:

`(x_2,y_2) = (6,80)`

Required

Express y as a function of x

First, calculate the slope:

`m = (y_2 - y_1)/(x_2 - x_1)`

This gives:

`m = (80 - 300)/(6 - 3)`

`m = (-220)/(3)`

`m = -(220)/(3)`

The equation is then calculated using:

`y = m(x - x_1) + y_1`

Where:

`m = -(220)/(3)`

`(x_1,y_1) = (3,300)`

`y = -(220)/(3)(x - 3) + 300`

Open bracket

`y = -(220)/(3)x + (220)/(3)*3 + 300`

`y = -(220)/(3)x + 220 + 300`

`y = -(220)/(3)x + 520`