# 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 $\displaystyle y = x$, you simply switch the x and y variables.

So $\displaystyle y = 2x + 3$ becomes

$\displaystyle x = 2y + 3$

$\displaystyle 2y = x - 3$

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

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

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

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

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

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

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