What is the equation of the line that is parallel to the given line and passes through the point (-2,2)

First we need to find the equation of the line that is given:

We can use the formula, [tex]m= \frac{ y_{1} - y_{2} }{ x_{1} - x_{2} } [/tex]

[tex] \frac{-3-(-4)}{0-(-5)} [/tex] = [tex] \frac{1}{5} [/tex]

So the equation for this line is [tex]y= \frac{1}{5} x - 3[/tex] 

This means that the equation for the line we are trying to find has a slope of [tex] \frac{1}{5} [/tex] as well

Lets put in the points in the equation and try to find the y-intercept:

[tex]2= \frac{1}{5} (-2) +b[/tex]
[tex] \frac{12}{5} =b[/tex]

So the final equation for the line we are trying to find is:

[tex]y= \frac{1}{5}x+ \frac{12}{5} [/tex]