Question

A car that travels along the highway to Denver at a steady speed. When it begins, it is 300 miles from Denver. After 3 hours, it is 180 miles from Denver. Which function describes the car's distance from Denver?

Answer 1

y=-40x-300

Explanation:

Answer 2

Answer:
`y=-40x+300`

Explanation:

This car follows a line, hence its motion can be modeled by the Line equation.

In fact, we already have two points of the line, if we call
`x` the time in hours and
`y` the traveled distance in miles:

Point 1:
`(x_(1),y_(1))=(0,300)`

Since we are told the car's initial position is 300 miles in the time 0 h

Point 2:
`(x_(2),y_(2))=(3,180)`

Since we are told the car's final position is 180 miles after 3h

Let's find the Slope
`m`:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=-40` This is the slope of the line

Now, the equation of the line is:

`y=mx+b`

We already know the slope, now we have to find the intersection point with the y-axis (
`b`) with any of the given points. Let's choose Point 1:
`(x_(1),y_(1))=(0,300)`

`300=-40(0)+b`

Isolating
`b`:

`b=-300`

Then, the equation of the line is:

`y=-40 x+300`