Question

Use the equation y = x - 2 and perform a reflection over the x-axis. Write an equation in 2

1

slope intercept form that represents the new line.

Answer 1

So after reflecting over the x-axis, the equation is:

`-y = x-2`

so the equation in the slope-intercept form

`-y = x-2`

`y=-x+2`

Here,

• The slope = m = -1

• The y-intercept = b = 2

Explanation:

Given the equation

`y = x - 2`

Reflecting over the x-axis inverts the sign of the y-coordinate, but the sign of the x-coordinate remains the same.

So after reflecting over the x-axis, the equation is:

`-y = x-2`

Now, writing the equation in the slope-intercept form

`y=mx+b`

where m is the slope and b is the y-intercept

so the equation in the slope-intercept form

`-y = x-2`

`y=-x+2`

Here,

• The slope = m = -1

• The y-intercept = b = 2