Answer: Choice B
y = (-3/2)x - 1
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Explanation:
The general slope intercept form is y = mx+b
The slope of the original line in the graph is m = 2/3. Flip the fraction and flip the sign to get -3/2 as the perpendicular slope. The original slope and perpendicular slope multiply to -1.
Since the perpendicular slope is -3/2, this narrows the choices between B and D.
We'll plug this perpendicular slope as the new m value, along with the coordinates of the point (-2,2). Then we solve for the y intercept b value.
So,
y = mx+b
2 = (-3/2)*(-2) + b
2 = -1.5*(-2) + b
2 = 3 + b
2-3 = b
-1 = b
b = -1
With m = -3/2 and b = -1, we have the final answer y = (-3/2)x-1 which is choice B
Side notes:
- Because -3/2 = -1.5, that equation in bold is the same as y = -1.5x-1
- The two perpendicular lines intersect at (0,-1). They both have the same y intercept. This won't always happen for any two random perpendicular lines.
- If you started at P(-2,2) and dropped down 3, and moved to the right 2, then you arrive at (0,-1).
