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A direct variation includes the points $(2,10)$ and $(1,n)$ . 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

(2,10)

and

(1,n)

. Find

n

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

\newline

n

= ____

Understand direct variation: Understand the concept of direct variation. In a direct variation, the relationship between two variables can be expressed as $y = kx$ , where $k$ is the constant of variation.
Find constant of variation: Use the given point $(2,10)$ to find the constant of variation $k$ . Substitute $x = 2$ and $y = 10$ into the direct variation equation $y = kx$ . $10 = k \times 2$
Solve for k: Solve for k. $\newline$ Divide both sides by $2$ to isolate k. $\newline$ $\frac{10}{2} = k$ $\newline$ $k = 5$
Write direct variation equation: Use the constant of variation $k$ to write the direct variation equation. $\newline$ Now that we know $k = 5$ , the direct variation equation is $y = 5x$ .
Find $n$ : Use the direct variation equation to find $n$ when $x = 1$ . Substitute $x = 1$ into the equation $y = 5x$ to find $n$ . $n = 5 \times 1$ $n = 5$

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