# What is the x- intercept and y- intercept of y= -4(x+2)?

Jun 15, 2018

The intercept with one axis is simply when the other variable goes to zero. So...

• The $x$-intercept is found by letting $y = 0$.

• The $y$-intercept is found by letting $x = 0$.

The result is shown in this graph:

graph{-4(x+2) [-11.04, 11.46, -10.585, 0.665]}

(x,y) = overbrace((-2","0))^"x-intercept", overbrace((0","-8))^"y-intercept"

Here is how I would do it.

$\underline{x - \text{intercept}}$

Let $y = 0$ and solve for $x$.

$0 = - 4 \left(x + 2\right)$

$0 = - 4 x - 8$

$4 x = - 8$

$x = - \frac{8}{4} = - 2$

As a result, the $x$-intercept is $\textcolor{b l u e}{\left(x , y\right) = \left(- 2 , 0\right)}$.

$\underline{y - \text{intercept}}$

One way to do this is to notice that in solving for the $x$-intercept, we got

$y = - 4 x - 8$

The $y = m x + b$ form of straight-line equations tells you that $b = - 8$ is the y-intercept right away, so that the coordinate is $\textcolor{b l u e}{\left(x , y\right) = \left(0 , - 8\right)}$ from the work shown above.

Another way to do it is by letting $x = 0$:

$y = - 4 \left(0 + 2\right)$

$= - 8$

As a result, the $y$-intercept is $\textcolor{b l u e}{\left(x , y\right) = \left(0 , - 8\right)}$.