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

Answer: $y=-40x+300$

Step-by-step 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 $m$:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=-40$  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:

$y=-40 x+300$

Answer 2

Answer:

y=-40x-300

Step-by-step explanation: