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A direct variation includes the points $(-20,-40)$ and $(7,n)$ . Find $n$ . Write and solve a direct variation equation to find the answer. $\newline$ $n = \_\_\_$

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Write and solve direct variation equations

Full solution

Q. A direct variation includes the points

(-20,-40)

and

(7,n)

. Find

n

. Write and solve a direct variation equation to find the answer.

\newline

n = \_\_\_

Identify Direct Variation Equation: Direct variation equation is $y = kx$ . We need to find $k$ using the given points $(-20,-40)$ .
Substitute Given Points: Substitute $x = -20$ and $y = -40$ into $y = kx$ to find $k$ . $\newline$ $-40 = k(-20)$
Solve for k: Divide both sides by $-20$ to solve for $k$ . $k = \frac{-40}{-20}$ $k = 2$
Finalize Direct Variation Equation: Now we have $k$ , so the direct variation equation is $y = 2x$ .
Find $n$ : To find $n$ , substitute $x = 7$ into $y = 2x$ . $\newline$ $n = 2(7)$ $\newline$ $n = 14$

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