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=-(10)/(2)x-(5)/(2) \\ y=-5x-(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.