Question

A line with equation $y=2x+3$ is reflected in the y-axis. Find an equation of the image line.

Short answer

The image line of the given equation is obtained as,

$y=-2x+3$

Step-by-step solution

Step 1. Given Information.

The given equation is $y=2x+3$.

Step 1. Concept Used.

When the equation is reflected about the y-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 x with $-x$ in the given equation.

$\begin{array}{l}y=2\cdot (-x)+3\\ y=-2x+3\end{array}$

Step 4. Conclusion.

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

$y=2x+3$