Question

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

A.
y = –2x – 9/4
B.
y = 2x – 3
C.
y = –1/2x – 3
D.
y = –1/2x + 3

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}*(-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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`\underline{\rule{300}{3}}`