Question

A line with equation $y=x+5$ is reflected in the x-axis. Find an equation of the image line.

Short answer

The image line of the given equation is obtained as,

$y=-x-5$

Step-by-step solution

Step 1. Given Information.

The given equation is $y=x+5$

Step 2. Concept Used.

When the equation is reflected about the x-axis $\left(x,y\right)$ becomes $\left(x,-y\right)$.

Step 3. Calculation.

The image line of the given equation can be obtained as,

Replacing y with $-y$ in the given equation.

$\begin{array}{c}-y=x+5\\ y=-x-5\end{array}$

Step 4. Conclusion.

Therefore, the image line of the given equation is obtained as,

$y=-x-5$