# Thread: Variables x and y related by an unconventional type of equation

1. ## Variables x and y related by an unconventional type of equation

The variables x and y are related by the equation . When the graph of against is drawn, a straight line is obtained which has a gradient of -5 and passes through the point (-2, 18).

Find the value of m and n.

2. Hello fterh
Originally Posted by fterh
The variables x and y are related by the equation . When the graph of against is drawn, a straight line is obtained which has a gradient of -5 and passes through the point (-2, 18).

Find the value of m and n.
We need to get an expression involving $\displaystyle \frac{y}{\sqrt x}$, so let's divide both sides by $\displaystyle \sqrt x$:
$\displaystyle \dfrac{y}{\sqrt x}= m + \dfrac nx$
$\displaystyle =n\cdot\dfrac 1x+m$
So when we plot the graph of $\displaystyle \frac{y}{\sqrt x}$ against $\displaystyle \frac{1}{x}$, the gradient is $\displaystyle n$. So:
$\displaystyle n=-5$
and if we plug this and the values $\displaystyle (-2, 18)$ into the equation, we get:
$\displaystyle 18=(-5)(-2)+m$

$\displaystyle \Rightarrow m = 8$

4. Edited: My bad, carless LOL.