Question

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

Answer 1

`y = (1)/(2)x +4`

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 = (y_2 - y_1)/(x_2 - x_1)`

`m = (4-0)/(8-0)`

`m = (4)/(8)`

`m = (1)/(2)`

So, the line has a slope of
`m = (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 = (1)/(2)(x - (-2))`

`y - 3 = (1)/(2)(x +2)`

Open bracket

`y - 3 = (1)/(2)x +1`

Make y the subject

`y = (1)/(2)x +1+3`

`y = (1)/(2)x +4`