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If
x and
y vary directly and
y is 2 when
x is 4 , find
y when
x is 6 .
Answer:
y=

If $x$ and $y$ vary directly and $y$ is $2$ when $x$ is $4$ , 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

vary directly and

y

is

2

when

x

is

4

, 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: Use the given values to find the constant of variation $k$ . We know that $y = 2$ when $x = 4$ . Substitute these values into the direct variation equation to find $k$ . $2 = k \times 4$
Solve for k: Solve for k. $\newline$ Divide both sides of the equation by $4$ to isolate k. $\newline$ $k = \frac{2}{4}$ $\newline$ $k = 0.5$
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 $y$ for $x=6$ : Use the direct variation equation to find $y$ when $x$ is $6$ . Substitute $x = 6$ into the equation $y = 0.5x$ to find $y$ . $y = 0.5 \times 6$ $y = 3$

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