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If
x and
y are in direct proportion and
y is 2 when
x is 8 , find
y when
x is 12 .
Answer:
y=

If $x$ and $y$ are in direct proportion and $y$ is $2$ when $x$ is $8$ , find $y$ when $x$ is $12$ . $\newline$ 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

2

when

x

is

8

, find

y

when

x

is

12

.

\newline

Answer:

y=

Establish Equation: Establish the direct variation equation. $\newline$ Since $x$ and $y$ are in direct proportion, we can write the relationship as $y = kx$ , where $k$ is the constant of proportionality.
Find Constant of Proportionality: Use the given values to find the constant of proportionality $k$ . We know that $y = 2$ when $x = 8$ . Substitute these values into the equation to find $k$ . $2 = k \times 8$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $8$ to isolate $k$ . $\newline$ k = rac{2}{8} $\newline$ k = rac{1}{4}
Write Equation with $k$ : Write the direct variation equation with the found value of $k$ . Now that we have $k = \frac{1}{4}$ , the direct variation equation is $y = \left(\frac{1}{4}\right)x$ .
Find $y$ for $x=12$ : Find $y$ when $x$ is $12$ . $\newline$ Substitute $x = 12$ into the direct variation equation $y = \frac{1}{4}x$ . $\newline$ $y = \frac{1}{4} \times 12$ $\newline$ $y = 3$

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