# The variables x=2 and y=7 varies directly. How do you write an equation that relates the variables and find y when x=8?

Nov 29, 2017

$y = 28$

#### Explanation:

“The variables $x = 2$ and $y = 7$ vary directly.”

We can express that as:

$y = m x$

$\setminus \rightarrow 7 = m \setminus \cdot 5$, where $m$ is the constant of variation (slope).

Now, we need to solve for $m$:

$7 = 2 m$

Divide both sides by $2$:

$m = \setminus \frac{7}{2}$

Now, we can plug this value, as well $x = 8$, into the next equation to find $y$:

$y = m x$

$\setminus \rightarrow y = \setminus \frac{7}{2} \setminus \cdot 8$

$\setminus \rightarrow y = \setminus \frac{56}{2}$

$\setminus \rightarrow y = 28$

Nov 29, 2017

$y = \frac{7}{2} x$
$y \left(8\right) = 28$

#### Explanation:

I assume you mean that $x \mathmr{and} y$ vary directly and $x = 2$ when $y = 7$

If so, then we know that:

$y = k x$ for some constant $k$

Since $x = 2$ when $y = 7$

$\therefore 7 = k \times 2$

$\to k = \frac{7}{2}$

Hence, $y = \frac{7}{2} x$ is our required equation.

We are asked to find $y$ when $x = 8$

$\to y \left(8\right) = \frac{7}{2} \times 8 = 7 \times 4$

$y \left(8\right) = 28$