Solve for y

An equation is not always given in slope-intercept form. The equation $2x+3y = 6$ describes a line, so it can be written as $y = mx+b$. To find that form, solve the equation for $y$, then divide each term:

$$2x+3y = 6$$

$$3y = -2x+6$$

$$y = \frac{-2x+6}{3}$$

$$y = \frac{-2}{3}x+2$$

Now you can read the slope, $\frac{-2}{3}$, and the y-intercept, (0, 2). The last step splits the fraction into two terms. Without it, the answer is correct, but you cannot read $m$ and $b$ from it.

For a nonvertical line, isolate y and simplify the right side to $mx+b$. The coefficient of x is the slope m, and the constant term is the y-intercept b.