# How do you graph using the intercepts for 2x+6y=0?

May 29, 2018

Refer to explanation below.

#### Explanation:

$2 x + 6 y = 0$

First rearrange the equation.
$2 x + 6 y = 0$
$6 y = 0 - 2 x$
$y =$ $\frac{- 2 x}{6}$

Now, substitute x = 0 into the equation to find the intersection with the y-axis.
$y = \frac{- \left(2 \cdot 0\right)}{6}$
$y = \frac{0}{6}$
$y = 0$
Therefore the graph intersects the y-axis at (0, 0)

Now, substitute y = 0 into the equation to find the intersection with the x-axis.
$0 = \frac{- \left(2 x\right)}{6}$
$6 \cdot 0 = - 2 x$
$\frac{0}{-} 2 = x$
Therefore the graph intersects the x-axis at (0, 0)

The gradient of the graph is found by looking at the coefficient of x.
$y = \frac{- \left(2 x\right)}{6}$
$y = \frac{- \left(1 x\right)}{3}$
$y = \left(- \frac{1}{3}\right) x$
Therefore the graph is observed to have a negative gradient with the value of $\frac{1}{3}$

graph{2x + 6y = 0 [-10, 10, -5, 5]}