What is the slope of a line that is perpendicular to the graph of 2x - 3y = 6?

Answer 1

Here's how to solve this problem from the beginning.

You are probably more familiar with 'slope intercept form' or y=mx+b. You just need to make that equation above look like the one right here, aka 'y' on one side and everything else on the other. Let's move some things around.

2x-3y=6

-3y=6-2x

3y=2x-6

y=2/3x-2

Now when you compare to y=mx+b (and you know 'm' is the slope), the slope of your original equation is 2/3!

In order to find the slope of a PERPENDICULAR LINE, it's very simple: two words, 'negative reciprocal'. AKA, flip the fraction upside down, and change positive to negative (and vice versa).

2/3 becomes -3/2 (because it started off as positive).

That's it!

Answer 2

The slope of the given line (graph) is 2/3 (-A/B, for the line given in general form Ax + By = C).

The opposite reciprocal slope is - 3/2, which is the slope of a line perpendicular to the given line.