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If
x and
y are in direct proportion and
y is 4 when
x is 8 , find
y when
x is 10 .
Answer:
y=

If $x$ and $y$ are in direct proportion and $y$ is $4$ when $x$ is $8$ , find $y$ when $x$ is $10$ . $\newline$ Answer: $y=$

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Write and solve direct variation equations

Full solution

Q. If

x

and

y

are in direct proportion and

y

is

4

when

x

is

8

, find

y

when

x

is

10

.

\newline

Answer:

y=

Write Equation: Write the equation that represents the direct variation between $x$ and $y$ . Since $y$ varies directly with $x$ , we can write the equation 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 $x = 8$ . Substitute these values into the direct variation equation to find $k$ . $4 = k \times 8$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $8$ to isolate $k$ . $\newline$ $k = \frac{4}{8}$ $\newline$ $k = 0.5$
Write Using $k$ : Write the direct variation equation using the value of $k$ . Now that we have found $k$ to be $0.5$ , we can write the direct variation equation as $y = 0.5x$ .
Find $y$ : Use the direct variation equation to find $y$ when $x$ is $10$ . Substitute $x = 10$ into the equation $y = 0.5x$ to find $y$ . $y = 0.5 \times 10$ $y = 5$

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