F fterh Jun 2010 21 0 Jun 19, 2010 #1 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.

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 MHF Hall of Honor Dec 2008 2,570 1,416 South Coast of England Jun 19, 2010 #2 Hello fterh fterh said: 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. Click to expand... 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

Hello fterh fterh said: 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. Click to expand... 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