Respuesta :
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]
