Question

Which equation represents a line that is perpendicular to y = 5x +2 and goes through

Answer 1

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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