How do you find the slope given -2x+3y=9?

1 Answer
Feb 1, 2016

To find the slope of a line, you must put the equation in the form of


where "m" represents the slope of the line.

To get to that form, you must solve for y in terms of x. Begin by isolating the y value on one side, here we add 2x to both sides.


Now that you have the y value all alone, you need to get rid of any coefficients, in this case, 3. You can choose to think of it as multiplying the ENTIRE equation by 1/3 or simply by dividing the ENTIRE equation by 3. Both do the exact same thing, its a personal preference whichever you use, just make sure what ever you do to one side you must do to the other.

So now we divide by three (or multiply by 1/3) and get:

We can see this equation is now in #y=mx+b# form with the value corresponding to #m# being #2/3#. This means the slop of the line is #2/3#. For future reference, the #b# in the equation is the y-intercept.