Question

What is the equation y=2x reflected across the y axis

Answer 1

`y = -2\, x`.

Explanation:

Find two points on the original line,
`y = 2\, x`:

Setting
`x = 0` gives
`y = 0`, which corresponds to the point
`(0,\, 0)`.

Setting
`x = 1` gives
`y = 2`, which corresponds to the point
`(1,\, 2)`.

Reflect the two points with respect to the
`y`-axis by inverting the
`x`-coordinate of each point. The point
`(0,\, 0)` stays the same, whereas the point
`(1,\, 2)` would be mapped to
`(-1,\, 2)`.

Find the equation of the new line. The slope of the new line would be:

`\begin{aligned}(2 - 0)/((-1) - 0) = (2)/((-1)) = -2\end{aligned}`.

Equation of the new line in point-slope form:

`y - 0 = (-2)\, (x - 0)`.

`y = -2\, x`.