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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
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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 [tex]\mathrm{-\cfrac{1}{2}}[/tex].

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

[tex]\mathrm{y=-\cfrac{1}{2}x+b}[/tex]. 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.)

[tex]\mathrm{-2=-\cfrac{1}{2}\times(-2)+b}[/tex].

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

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

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

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

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

Best Regards!

[tex]\star\bigstar\underline{\underline{\overline{\overline{\bold{Reach\:Far.\:Aim\:high.\:Dream\:big.}}}}}\bigstar\star[/tex]

[tex]\underline{\rule{300}{3}}[/tex]
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