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If
x and
y are in direct proportion and
y is 14 when
x is 2 , find
y when
x is 9 .
Answer:
y=

If $x$ and $y$ are in direct proportion and $y$ is $14$ when $x$ is $2$ , find $y$ when $x$ is $9$ . $\newline$ 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

14

when

x

is

2

, find

y

when

x

is

9

.

\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 $y = 14$ when $x = 2$ . Substitute these values into the direct variation equation to find $k$ . $14 = k \times 2$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $2$ to isolate k. $\newline$ $\frac{14}{2} = \frac{k \times 2}{2}$ $\newline$ $k = 7$
Write Updated Equation: Write the direct variation equation using the value of $k$ . $\newline$ Now that we know $k = 7$ , the direct variation equation is $y = 7x$ .
Find $y$ for $x=9$ : Find $y$ when $x = 9$ . $\newline$ Substitute $x = 9$ into the direct variation equation to find $y$ . $\newline$ $y = 7 \times 9$ $\newline$ $y = 63$

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