What is the equation when y equals 2x plus 2 is reflected over the y axis?

Answer 1

First let's look at what y=2x+2 looks like. It is the equation of a line with slope 2 and y intercept 2.

When we reflect across the y axis, the point (x,y) become (-x,y).

Remember that when you reflect across the x axis (x,y) become (x,-y) and when you reflect across the y axis (x,y) becomes (-x,y)

So one way to do this problem is algebraically. The slope cannot change values but must change sign with the reflection about the y axis. Let's take a point, not on the y axis, but on the line. (the point (0,2) is the one on the y axis and it would not change). Take (1,4) and note that after reflection the point is (-1,4). So we have a line with point (-1,4) and slope -2. Put this in point slope form and we have y-4=-2(x+1) or

y-4=-2x-2 which in slope intercept form is y=-2x+2.

The equation of the reflected line is y=-2x+2

So the original line was y=2x+2 and the reflected line is y=-2x+2. The y intercept is the same. Look at a few points. The point (5,12) was on the original line, and

(-5,12) is on the reflected line. (2,4) was on the original one and (-2,4) is on the new one.

We could have done this all geometrically without the algebra. The line we started with was y=2x+2. If we reflect across the y axis, we cannot change the y intercept, but the slope must become it's negative. The y values remain unchanged, Right away we could write the equation y=-2x+2. This would change the slope to -2 and the y intercept would remain the same, 2.

You can also graph the original line on graph paper, reflect it and note the new slope and the y intercept. This would be another way to find the answer. Sometimes we want the value of points when reflected across axes or even arbitrary lines. Matrices are often used for this. The matrix below will transform a point across the y axis.

|-1 0x|

|0 1y|