Variables x and y related by an unconventional type of equation

**fterh** · June 18th 2010, 11:18 PM

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.

**Grandad** · June 18th 2010, 11:58 PM

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 $\frac{y}{\sqrt x}$ , so let's divide both sides by $\sqrt x$ :

$\dfrac{y}{\sqrt x}= m + \dfrac nx$

$=n\cdot\dfrac 1x+m$

So when we plot the graph of $\frac{y}{\sqrt x}$ against $\frac{1}{x}$ , the gradient is $n$ . So:

$n=-5$

and if we plug this and the values $(-2, 18)$ into the equation, we get:

$18=(-5)(-2)+m$

$\Rightarrow m = 8$

Grandad

**fterh** · June 19th 2010, 12:04 AM

Genius

Thanks grandad

**fterh** · June 19th 2010, 12:37 AM

Edited: My bad, carless LOL.

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