A quick solution is to sketch the given line, and then sketch a perpendicular line.

To sketch the line given by the equation \(-2x + 3y = 6\), we need only find two points that satisfy the equation.
Let's plug in some EASY values.

If x = 0, then we get: \(-2(0) + 3y = 6\)
When we solve this for y, we get: y = 2
So, one point on the line is (0, 2)

Let's now find a second point.
If y = 0, then we get: \(-2x + 3(0) = 6\)
When we solve this for x, we get: x = -3
So, another point on the line is (-3, 0)

We can now plot both points and draw our line:




Notice that the line has a POSITIVE slope.
This means that any line that's PARALLEL with the line will also have a POSITIVE slope.




Conversely, any line that's PERPENDICULAR to the line will also have a NEGATIVE slope.


So, we get:
QUANTITY A: some NEGATIVE slope
QUANTITY B: some POSITIVE slope

Answer: B

Cheers,
Brent

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