Answer: Choice A. y + 5 = -2(x + 2)
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Step-by-step explanation:
Let's solve the given equation for y so we can find the slope.
3x - 6y = 2
3x = 2+6y
3x-2 = 6y
6y = 3x-2
y = (3x-2)/6
y = (3x/6) - (2/6)
y = (1/2)x - 1/3
The last equation is in y = mx+b form. We see that m = 1/2 is the slope.
Apply the negative reciprocal to go from 1/2 to -2/1 or just -2.
The original slope is 1/2, and the perpendicular slope is -2.
Rule: multiplying any two perpendicular slopes leads to -1 where neither line can be vertical.
Let's plug in m = -2, x1 = -2 and y1 = -5 into point slope form
y - y1 = m(x - x1)
y - (-5) = -2(x - (-2))
y + 5 = -2(x + 2)