# What are the intercepts of -y=3y-6x-9?

Apr 12, 2016

$y$-intercept is $\left(0 , 2.25\right)$

$x$-intercept is $\left(- 1.5 , 0\right)$

#### Explanation:

The $y$-intercept is the point where the line cuts the $y$-axis.
This means, we have to find the point when $x = 0$.

Similarly, the $x$-intercept is the point where the line cuts the $x$-axis. i.e. to find the point when $y = 0$.

Pretty simple.

Here, first let's write the equation in terms of $y$.

$- y = 3 y - 6 x - 9$

$\implies - 3 y - y = - 6 x - 9$

Multiply both sides by $- 1$

$\implies 3 y + y = 6 x + 9$

$\implies 4 y = 6 x + 9$

$\implies y = \frac{6 x + 9}{4}$

Below is a step-by-step to work out the $y$-intercept and $x$-intercept .

The graph shows the line cutting the two axes.