The variables x and y are related by the equation y=ax/(x-b),where a and b are constants .When y is plotted against y/x ,a straight line is obtained .The line has gradient 3 and y-intercept 2.

Question

The variables x and y are related by the equation y=ax/(x-b),where a and b are constants .When y is plotted against y/x ,a straight line is obtained .The line has gradient 3 and y-intercept 2.
(i)Find the values of a and b 
(ii)Find the values of x which x=y

Steve · Answer

y/x = a/(x-b) the given line has equation (slope-intercept) y = 2 + 3(y/x) xy = 2x + 3y y = 2x/(x-3) so, a=2 b=3 if x=y, y = 2+3 = 5 check: 5 = 2*5/(5-3)