# Are the graphs 2y=4x-16 and  y=2x-8 perpendicular?

Mar 31, 2017

These are equations of the same line.

#### Explanation:

$2 y = 4 x - 16 \mathmr{and} y = 2 x - 8$

Write the first one in the form $y = m x + c$ as well. (div2)

$y = 2 x - 8 \mathmr{and} y = 2 x - 8$

We see that there is actually only one line.

If there were 2 lines, they would have been parallel because the gradients are the same.

$y = \textcolor{red}{2} x + 5 \mathmr{and} y = \textcolor{red}{2} x - 8$ are parallel

$y = \textcolor{b l u e}{- \frac{1}{2}} x - 8 \mathmr{and} y = \textcolor{b l u e}{2} x - 8$ are perpendicular.

$\textcolor{b l u e}{- \frac{1}{2} \times \frac{2}{1}} = - 1$