# How do you graph y=-1/2x-5 using intercepts?

Apr 26, 2017

x-intercept: $\left(- 10 , 0\right)$
y-intercept: $\left(0 , - 5\right)$

#### Explanation:

To start off, we know that intercepts only exist when the x-coordinate or y-coordinate of a point equal 0.

So we look into the given function:

$y = - \frac{1}{2} x - 5$

To find the y-intercept, the x-coordinate has to equal 0, so let's plug in 0 into the function.

$y = - \frac{1}{2} \cdot 0 - 5$

$y = - 5$

So now we know when $x = 0$, $y = - 5$. So we have a point $\left(0 , - 5\right)$ on the graph.

For the x-intercept, the y-coordinate has to equal 0. We plug it in to get:

$0 = - \frac{1}{2} x - 5$

$\frac{1}{2} x = - 5$

$x = - 10$

So we now have the x intercept at point $\left(- 10 , 0\right)$

Here's a graph for reference:

graph{y = -1/2x-5 [-13, 7, -6.96, 3.04]}