Question

Are y=-5x-2 and -10x-2y=5 perpendicular? explain

Answer 1

Two lines are perpendicular if and only if:

$m_1m_2=-1$

Then we need to find the slopes of each of them. We know that the slope-intercept form is:

$y=mx+b$

Then, comparing the first equation with the general form we have that:

$m_1=-5$

Now, to find the slope of the second equation we first solve it for y:

$\begin{gathered} -10x-2y=5 \\ -10x-5=2y \\ y=-\frac{10}{2}x-\frac{5}{2} \\ y=-5x-\frac{5}{2} \end{gathered}$

Then:

$m_2=-5$

Now we make the product:

$m_1m_2=(-5)(-5)=25$

Since the slopes don't fullfil the condition we condlude that the lines are not perpendicular.