Hello, Rachel,
A perpendicular line would have the negative of the inverse slope of the original line. The slope of y = 3x-2 is 3. A perpendicular line would have a slope of -(1/3).
That would eliminate options c and d.
The next step is to determine the value of the y intercept, where x = 0.
We are given an actual data point of (-2,3), so let's use that in an equation that has the slope we determined above:
y = -(1/3)x + b
For point (-2,3):
3 = -(1/3)*(-2) + b
b = 2(1/3), or 7/3
So the equation should read y = -(1/3)x + 7/3. That looks like choice A.
You can confirm it by drawing both lines on a graph and observing that they are perpendicular to each other and that the second does go through point (-2,3).
Bob
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