# If y varies directly as x and y =5 when x=2, how do you find y when x=6?

May 12, 2018

The relationship between x and y is $y = \frac{5}{2} x$, therefore $y = 15$ when $x = 6$

#### Explanation:

The way I read your question is that we can write the relation between x and y on the form $y = a x$.

In this case we know that $5 = a \cdot 2$ or $a = \frac{5}{2}$, so that the relationship between y and x can be written on the form
$y = \frac{5}{2} x$.

In that case we can just plug in x=6 in the equation, in which case we get
$y = \frac{5}{2} \cdot 6 = 15$

An easy way of finding the same result is with a graph:
graph{y=5/2x [-9.67, 30.87, -1.92, 18.34]}

Reading off our graph we can see that the line goes through (2, 5) and (6, 1).