Variables x and y related by an unconventional type of equation

Jun 2010
21
0
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

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

\(\displaystyle \Rightarrow m = 8\)​
Grandad
 
Jun 2010
21
0
Edited: My bad, carless LOL.
 
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