Question

The line with equation y = 2 x + 3 is reflected in the x -axis. Which of the following is the equation of the new line?

Answer 1

The equation of the new line is
`y = -2x - 3`

Explanation:

Reflecting a function over the x-axis:

Suppose we have a function y = f(x)

Suppose y' is the function y, reflected over the x-axis. Their relation is:

y' = -y

In this question:

Line with equation
`y = 2x + 3`

Reflection over the x-axis:

We have that:

`y = -(2x + 3) = -2x - 3`

The equation of the new line is
`y = -2x - 3`