Question

Which equation represents the line that is parallel to segment RS in the triangle below and passes through point T?

Answer 1

Answer:

$y = \frac{1}{2}x +4$

Step-by-step explanation:

Given:

$R = (0,0)$

$S= (8,4)$

$T = (-2,3)$

First, we have that the line is parallel to RS.

This means that the line has the same slope as RS and the slope of RS is calculated as follows:

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

$m = \frac{4-0}{8-0}$

$m = \frac{4}{8}$

$m = \frac{1}{2}$

So, the line has a slope of $m = \frac{1}{2}$

Next, we have that the line passes through $T = (-2,3)$.

The equation of the line is then calculated using the following formula

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

$y - 3 = \frac{1}{2}(x - (-2))$

$y - 3 = \frac{1}{2}(x +2)$

Open bracket

$y - 3 = \frac{1}{2}x +1$

Make y the subject

$y = \frac{1}{2}x +1+3$

$y = \frac{1}{2}x +4$