# How do you graph using slope and intercept of 6x + 5y = 2?

Apr 11, 2017

See below:

#### Explanation:

First, rewrite it in slope intercept form: $y = m x + b$:

Subtract $6 x$ on both sides:

$5 y = 2 - 6 x$

Now divide by $5$

$y = \frac{2}{5} - \frac{6}{5} x$

Rewrite it so the $x$ comes first:

$y = - \frac{6}{5} x + \frac{2}{5}$

Now our equation is in the form $y = m x + b$. The $m$ which is $- \frac{6}{5}$ represents the slope and the $\frac{2}{5}$ represents the y-intercept. So make a point on $\left(0 , \frac{2}{5}\right)$ and then move left $6$ units of $x$ and go up $5$ units of $y$. Then, connect the dots:

graph{y=(-6/5)x+(2/5) [-10, 10, -5, 5]}