# How do you calculate the slope, x intercept, and y intercept of the following equation: 3x+6y = 9?

Jul 31, 2015

The slope is $- \frac{1}{2}$.
The y-intercept is $\frac{3}{2}$.
The x-intercept is $3$.

#### Explanation:

Get the equation into slope-intercept form $y = m x + b$ by solving for $y$. In the equation $y = m x + b$, $m$ is the slope, and $b$ is the y-intercept.

$6 y = - 3 x + 9$

Divide both sides by $6$.

$y = - \frac{3}{6} x + \frac{9}{6}$ =

$y = - \frac{1}{2} x + \frac{3}{2}$

The slope is $- \frac{1}{2}$ and the y-intercept is $\frac{3}{2}$.

To find the x-intercept, set $y$ to zero, and solve for $x$.

$0 = - \frac{1}{2} x + \frac{3}{2}$

Subtract $\frac{3}{2}$ from both sides.

$- \frac{3}{2} = - \frac{1}{2} x$

Multiply both sides times $2$.

$- 3 = - x$

Multiply both sides times $- 1$.

$3 = x$

The x-intercept is $3$.

graph{3x+6y=9 [-10, 10, -5, 5]}