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?

Answers

Answer 1

Answer:

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 $m$ :

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

$m=-40$ 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:

Answer:

y=-40x-300

Step-by-step explanation:

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Answers

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Answers

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