Answer:
a= 2.5, b= 5
Step-by-step explanation:
Since the graph is obtained by plotting y against xy, Y= y and X= xy. (Linear law: Y=mX +c)
Given that the line intersects the vertical axis at (0, ½), the y-intercept is ½.
Equation of the line: Y= mX +½
Given that the gradient is ⅕, m= ⅕.
Y= ⅕X +½
Substitute Y= y and X=xy:
y= ⅕xy +½
Rewrite the equation such that it is in the form of [tex]y = \frac{a}{b - x} [/tex]:
[tex]y - \frac{1}{5} xy = \frac{1}{2} [/tex]
Factorise y out on the left hand side:
[tex]y(1 - \frac{1}{5} x) = \frac{1}{2} [/tex]
Make y the subject of formula:
[tex]y = \frac{1}{2} \div (1 - \frac{1}{5} x) \\ y = \frac{1}{2} \div ( \frac{5}{5} - \frac{x}{5} ) \\ y = \frac{1}{2} \div \frac{5 - x}{5} \\ y = \frac{1}{2} \times \frac{5}{5 - x} \\ y = \frac{5}{2(5 - x)}[/tex]
Do not expand at this step as the coefficient of x in the equation is 1. Instead, divide both the numerator and denominator by 2.
[tex]y = \frac{2.5}{5 - x} [/tex]
Thus, a= 2.5 and b= 5.
