Question

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

Answer 1

Answer:

$y = -2\, x$.

Step-by-step 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:

$\begin{aligned}\frac{2 - 0}{(-1) - 0} = \frac{2}{(-1)} = -2\end{aligned}$.

Equation of the new line in point-slope form:

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

$y = -2\, x$.