# How do you find the slope and intercept of 3x+7y=4?

Oct 31, 2015

You change the equation into slope-intercept form ($y = m x + b$).

#### Explanation:

$3 x + 7 y = 4$
You need to isolate the y by subtracting $3 x$ from each side.
$7 y = 4 - 3 x$
Then, to get rid of the $7 y$ and make it a single $y$, you divide each side by seven.
$y = \frac{4 - 3 x}{7}$
You divide four by seven, and three x by seven.
$y = \frac{4}{7} - \frac{3}{7} x$
Move the $4 x$ to have the equation in $y = m x + b$ form.
$y = - \frac{3}{7} x + \frac{4}{7}$
The slope is $- \frac{3}{7}$ and the y-intercept is $\frac{4}{7}$.