The equation in slope-intercept form is x – 5y = -12
Given,
y = -5x – 8
This is in slope-intercept form, y = mx + b
Where, m is slope and b is y-intercept.
Here, m = -5
Perpendicular lines have slopes that are negative reciprocals, [tex]m_{p}[/tex] = -1/m
Here we need equation of line through (-2, 2) with slope -1/-5 = 1/5
y = (1/5)x + b
where (-2, 2) is on the line.
2 = 1/5(-2) + b
2 = -2/5 + b
b = 2 + 2/5 = 12/5
therefore, equation we need is:
y = 1/5x + 12/5
that is,
1/5x – y = -12/5
Multiplying 5 in both sides, we get
5(1/5x) – 5y = (-12/5)5
That is, the equation we need is:
x – 5y = 12
Learn more about slope-intercept form here: https://brainly.com/question/14344772
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