Question

Ye is riding home from a friend's house. After 5 minutes he is 4 miles from home, after 15 minutes Ye is 2 miles from home. Which equation models his distance from home y, in terms of minutes, x?

Answer 1

Answer:

$y = -\frac{1}{5}x + 5$

Step-by-step explanation:

Given

$5\ minutes = 4\ miles$

$15\ minutes = 2\ miles$

Required

Determine the equation

y represents distance

x represents time

So, the given parameters can be modeled (x,y) as:

$(x_1,y_1) = (5,4)$

$(x_2,y_2) = (15,2)$

First, we need to determine the slope of the function.

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{2 - 4}{15 - 5}$

$m = \frac{-2}{10}$

$m = -\frac{1}{5}$

The equation can be determined using:

$y - y_1 = m(x - x_1)$

Where

$m = -\frac{1}{5}$

$(x_1,y_1) = (5,4)$

$y - y_1 = m(x - x_1)$

becomes

$y - 4 = \frac{-1}{5}(x - 5)$

Open bracket

$y - 4 = -\frac{1}{5}x + 1$

Solve for y

$y = -\frac{1}{5}x + 1 + 4$

$y = -\frac{1}{5}x + 5$