The equation of the line that is parallel to the given line and passes through the point (-2,2) is:
[tex]y = \frac{x}{5} + \frac{12}{5}[/tex]
A linear function is modeled by:
y = mx + b
In which:
When two lines are parallel, they have the same slope. In this problem, the given line passes through (-5,-4) and (0,-3), hence the slope is:
m = (-3 - (-4))/(0 - (-5)) = 1/5.
Hence the equation is:
[tex]y = \frac{x}{5} + b[/tex]
When x = -2, y = 2, then:
[tex]y = \frac{x}{5} + b[/tex]
[tex]2 = \frac{-2}{5} + b[/tex]
[tex]b = \frac{12}{5}[/tex]
Hence:
[tex]y = \frac{x}{5} + \frac{12}{5}[/tex]
More can be learned about linear equations at https://brainly.com/question/24808124
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