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If
x and
y are in direct proportion and
y is 5 when
x is 15 , find
y when
x is 6 .
Answer:
y=

If $x$ and $y$ are in direct proportion and $y$ is $5$ when $x$ is $15$ , find $y$ when $x$ is $6$ . $\newline$ 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

5

when

x

is

15

, find

y

when

x

is

6

.

\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 $y = 5$ when $x = 15$ . Substitute these values into the direct variation equation to find $k$ . $5 = k \times 15$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $15$ to isolate $k$ . $\newline$ $k = \frac{5}{15}$ $\newline$ $k = \frac{1}{3}$
Write Updated Equation: Write the direct variation equation with the found value of $k$ . Now that we have found $k$ to be $\frac{1}{3}$ , we can write the direct variation equation as $y = \left(\frac{1}{3}\right)x$ .
Find $y$ for $x=6$ : Use the direct variation equation to find $y$ when $x$ is $6$ . Substitute $x = 6$ into the equation $y = \frac{1}{3}x$ . $y = \frac{1}{3} \times 6$ $y = 2$

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