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3 years ago

A direct variation function contains the points (-9, -3) and (-12, -4) Which equation represents the function?

Mathematics

1 answer:

Bezzdna [24]3 years ago

8 0

Answer:

y = $\frac{1}{3}$ x

Step-by-step explanation:

Given that y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use either of the 2 given points

Using (- 9, - 3), then

k = $\frac{y}{x}$ = $\frac{-3}{-9}$ = $\frac{1}{3}$

y = $\frac{1}{3}$ x ← equation of function

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$\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2\qquad center~~(\stackrel{-7}{ h},\stackrel{-1}{ k})\qquad \qquad radius=\stackrel{17}{ r}\\\\\\\[x-(-7)]^2+[y-(-1)]^2=17^2\implies (x+7)^2+(y+1)^2=289\\\\\\\stackrel{\textit{since we know x = -15}}{(-15+7)^2+(y+1)^2=289}\implies (-8)^2+\stackrel{FOIL}{(y^2+2y+1^2)}=289\\\\\\64+y^2+2y+1=289\implies y^2+2y=224\implies y^2+2y-224=0\\\\\\(y+16)(y-14)=0\implies y=\begin{cases}-16\\14\end{cases}$

since it's a circle, it touches x = -15 twice, check the picture below.

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Answer:

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Step-by-step explanation:

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