Answer:
[tex]y = \frac{1}{2}x +4[/tex]
Step-by-step explanation:
Given:
[tex]R = (0,0)[/tex]
[tex]S= (8,4)[/tex]
[tex]T = (-2,3)[/tex]
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:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{4-0}{8-0}[/tex]
[tex]m = \frac{4}{8}[/tex]
[tex]m = \frac{1}{2}[/tex]
So, the line has a slope of [tex]m = \frac{1}{2}[/tex]
Next, we have that the line passes through [tex]T = (-2,3)[/tex].
The equation of the line is then calculated using the following formula
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - 3 = \frac{1}{2}(x - (-2))[/tex]
[tex]y - 3 = \frac{1}{2}(x +2)[/tex]
Open bracket
[tex]y - 3 = \frac{1}{2}x +1[/tex]
Make y the subject
[tex]y = \frac{1}{2}x +1+3[/tex]
[tex]y = \frac{1}{2}x +4[/tex]
