Question

Graph each equation by using the $x$- and $y$-intercepts.

$y=-x-5$

Short answer

The graph of the equation $y=-x-5$is:

Step-by-step solution

Step 1. Find the x and y- intercepts of the equation y=−x−5.

To find the -$x$intercept, substitute 0 for $y$and find the value of $x$.

$$\begin{gathered} y=-x-5 \\ 0=-x-5 \\ x=-5 \end{gathered}$$

Therefore, the $x$-intercept is $-5$.

As, the $x$-intercept is$-5$that means the graph of$y=-x-5$will intersect the $x$-axis at $\left(-5,0\right)$.

To find the $y$-intercept, substitute 0 for$x$and find the value of $y$.

$\begin{array}{l}y=-x-5\\ y=-0-5\\ y=-5\end{array}$

Therefore, the $y$-intercept is $-5$.

As, the $y$-intercept is$-5$that means the graph of$y=-x-5$will intersect the $y$-axis at $\left(0,-5\right)$.

Step 2. Draw the graph of the equation y=−x−5.

Draw the graph of the equation$y=-x-5$ by using the information that the graph of the equation$y=-x-5$ is a line passing through the points$\left(-5,0\right)$ and $\left(0,-5\right)$.

Therefore, the graph of the equation$y=-x-5$ is: