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

Feb 1, 2016

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

$y = m x + b$

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.

$3 y = 2 x + 9$

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:

$y = \frac{2}{3} x + 3$
We can see this equation is now in $y = m x + b$ form with the value corresponding to $m$ being $\frac{2}{3}$. This means the slop of the line is $\frac{2}{3}$. For future reference, the $b$ in the equation is the y-intercept.