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If
x and
y vary directly and
y is 4 when
x is 2 , find
y when
x is 5 .
Answer:
y=

If $x$ and $y$ vary directly and $y$ is $4$ when $x$ is $2$ , find $y$ when $x$ is $5$ . $\newline$ Answer: $y=$

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Write and solve direct variation equations

Full solution

Q. If

x

and

y

vary directly and

y

is

4

when

x

is

2

, find

y

when

x

is

5

.

\newline

Answer:

y=

Write Equation: Write the equation that represents the direct variation between $x$ and $y$ . Since $y$ varies directly with $x$ , the equation can be written as $y = kx$ , where $k$ is the constant of variation.
Find Constant: Use the given values to find the constant of variation $k$ . We know that $y = 4$ when $x = 2$ . Substitute these values into the direct variation equation to find $k$ . $4 = k \times 2$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $2$ to isolate k. $\newline$ $k = \frac{4}{2}$ $\newline$ $k = 2$
Write with $k$ : Write the direct variation equation with the found value of $k$ . Now that we know $k = 2$ , the direct variation equation is $y = 2x$ .
Find $y$ : Use the direct variation equation to find $y$ when $x$ is $5$ . Substitute $x = 5$ into the equation $y = 2x$ . $y = 2 \times 5$ $y = 10$

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