Answer:
y = -1/5x + 1
Step-by-step explanation:
By definition, the product of the slopes of two perpendicular lines, neither of which is vertical, is always -1.
Given the linear equation, y = 5x + 2, and the point (-10, 3):
Since the slope of the original linear equation is 5, then it means that the slope of the perpendicular line must be -1/5 (because if you multiply -1/5 by 5, the result is -1).
Therefore, the slope of the perpendicular line is -1/5.
Next, we'll use the slope of the perpendicular line and the coorindates of the given point, (-10, 3). Let (x1, y1) = (-10, 3)
We'll plug these values into the point-slope form:
y - y1 = m(x - x1)
y - 3 = -1/5[x - (-10)]
y - 3 = -1/5(x + 10)
y - 3 = -1/5x - 2
Add 3 on both sides to isolate the y:
y - 3 + 3 = -1/5x - 2 + 3
y = -1/5x + 1
Therefore, the equation of the line that is perpendicular to y = 5x + 2 is:
y = -1/5x + 1
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