Question

Find the equation of the line through the point (–2, –2) that is perpendicular to the line y = 2x – 1.

Answer 1

Hi student, let me help you out!

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Part 1.

Perpendicular lines have slopes that are opposite inverses of each other.

The opposite inverse of 2 is $\mathrm{-\cfrac{1}{2}}$.

Now let's stick in this number into the equation $\mathrm{y=mx+b}$:

$\mathrm{y=-\cfrac{1}{2}x+b}$.  Let's carry out several operations to determine the y intercept.

First, let's stick in -2 for x and y (Do you remember that the line passes through (-2,-2)? We're given that piece of information.)

$\mathrm{-2=-\cfrac{1}{2}\times(-2)+b}$.

You are probably thinking, "Why did you do that and just complicate things?" Wait for it! ^-^

Upon simplifying this, we obtain: $\mathrm{-2=1+b}$. See, it's nice and smooth now.

One last operation remains. We need to subtract 1 from both sides: $\mathrm{-3=b}$.

∴, the equation of the line is: $\mathrm{\underline{\boxed{y=-\cfrac{1}{2}-3}}}$

Hope this helped you out, ask in comments if any queries arise.

Best Regards!

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