# Thread: reflection in the line y = x+1???

1. ## reflection in the line y = x+1???

If the line y = 2x+3 is reflected in the line y = x+1, find what its equation becomes.

2. Originally Posted by usagi_killer
If the line y = 2x+3 is reflected in the line y = x+1, find what its equation becomes.
When you reflect a line over $y = x$, you simply switch the x and y variables.

So $y = 2x + 3$ becomes

$x = 2y + 3$

$2y = x - 3$

$y = \frac{1}{2}x - \frac{3}{2}$

The resulting equation of a line is also known as the inverse of the original equation.

In the problem, the line was reflected over $y = x + 1$, so you add $1$ to the inverse of the original equation.

$y = \frac{1}{2}x - \frac{3}{2} + 1$

$y = \frac{1}{2}x - \frac{1}{2}$

If you drew $y = 2x+3$ and $y = \frac{1}{2}x - \frac{1}{2}$ on graph paper and folded the paper at $y = x + 1$, the two lines should be right on top of each other.