Question

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

Answer 1

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

`y=mx+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.

`3y=2x+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=2/3x+3`
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.