# How do you find the slope of  3y=x+3?

Jul 13, 2016

Slope: $\frac{1}{3}$

#### Explanation:

Slope-intercept form: $y = m x + b$; where $m$ is the slope.

If we put the given equation into slope-intercept form, we can identify the slope.

First get $y$ all by itself.

$3 y = x + 3$

$y = \frac{x}{3} + 1$

This equation is now in slope intercept form. We must find the slope. We saw at the top that the slope, $m$, comes right before the variable. Here is our variable term:

$\frac{x}{3}$

It is in the form of a fraction. What do we do to clearly identify the slope? Rewrite the variable term, since $\frac{x}{3}$ is the same as $\frac{1}{3} \times x$.

$\frac{x}{3} = \frac{1}{3} \times x = \frac{1}{3} x$

Now let's rewrite the whole equation.

$y = \frac{1}{3} x + 1$

$\textcolor{g r e y}{y = m x + b}$

Look for the number before $x$, or the number combined with it. In this case, the slope appears to be $\frac{1}{3}$.

If we were to graph the equation and look at the slope that way, it would be the same.

graph{1/3x+1 [-10, 10, -5, 5]}