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

#### 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.

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Hello 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:
$$\displaystyle 18=(-5)(-2)+m$$

$$\displaystyle \Rightarrow m = 8$$​