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A direct variation includes the points $(3,15)$ 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

(3,15)

and

(1,n)

. Find

n

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

\newline

n = \_\_\_

Select equation direct variation: Select the equation that represents direct variation. $\newline$ Since $y$ varies directly with $x$ , we use the direct variation equation: $y = kx$ .
Find constant proportionality: Use the given point $(3,15)$ to find the constant of proportionality $(k)$ . Substitute the values in $y = kx$ . Plug in $3$ for $x$ and $15$ for $y$ in $y = kx$ . $15 = k \times 3$
Solve constant proportionality: Solve for the constant of proportionality $k$ . $\newline$ Divide both sides by $3$ to isolate $k$ . $\newline$ $\frac{15}{3} = \frac{(k \times 3)}{3}$ $\newline$ $5 = k$ $\newline$ $k = 5$
Write direct variation equation: Write the direct variation equation using the value of $k$ . $\newline$ Since $k = 5$ , the direct variation equation is $y = 5x$ .
Find $n$ : Use the direct variation equation to find $n$ when $x = 1$ . Substitute $1$ for $x$ in $y = 5x$ to find $n$ . $n = 5 \times 1$ $n = 5$

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