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If
x and
y are in direct proportion and
y is 9 when
x is 12 , find
y when
x is 8 .
Answer:
y=

If $x$ and $y$ are in direct proportion and $y$ is $9$ when $x$ is $12$ , find $y$ when $x$ is $8$ . $\newline$ 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

9

when

x

is

12

, find

y

when

x

is

8

.

\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 of Variation: Use the given values to find the constant of variation $k$ . We know that $y = 9$ when $x = 12$ . Substitute these values into the direct variation equation to find $k$ . $9 = k \times 12$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $12$ to isolate k. $\newline$ $k = \frac{9}{12}$ $\newline$ $k = \frac{3}{4}$
Write Using Value of $k$ : Write the direct variation equation using the value of $k$ . Now that we have found $k$ to be $\frac{3}{4}$ , we can write the direct variation equation as $y = \left(\frac{3}{4}\right)x$ .
Find $y$ : Find $y$ when $x$ is $8$ . $\newline$ Substitute $x = 8$ into the direct variation equation $y = \frac{3}{4}x$ . $\newline$ $y = \frac{3}{4} \times 8$ $\newline$ $y = 6$

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