Question

What is the equation of a line that is perpendicular to the line y = 2x + 4 and passes through the point (–2, 3)?

Group of answer choices


y = -1/2 x + 2


y = −1/2 x + 4


y = 2x + 4


y = 2 x + 2
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Answer 1

A. y = -1/2x + 2

Explanation:

Step 1:The slope of the given line is m = 2

Step 2: The perpendicular slope (m1) is the negative reciprocal of the slope m

m1 = -1/m = -1/2

So the perpendicular line will have a slope of m1 = -1/2

Step 3: Now we have a point and the slope so we can use point-slope form, which is:

y - y0 = m1 (x - x0)

In this equation we have: m1 = -1/2, x0 = -2 and y0 = 3. After substitution we have:

y - 3 = -1/2 (x - ( -2) )

let's solve for: -1/2 (x - ( -2) )

-1/2 (x - ( -2) ) = (-1/2) (x + 2) = (-1/2) * (x) + ( -1/2) * (2) = -1/2x - 1

y - 3 = -1/2x - 1

y - 3 + 3 = -1/2x - 1 + 3

y = -1/2x + 2