Question

I have difficulty doing this question. Please help, thanks. :)

The variables x and y are related in such a way that when y^2 is plotted against x^2y, a straight line is obtained which passes through the points (3,5) and (5,9)


(a) Express x in terms of y

(b) Find the two values of y for which x = 1/2 √5


Thanks.

I assume x^2y means (x²)y and not x^(2y). For a linear relationship, w = mz + b, where m is the slope and b is the intercept. If you have 2 points you can figure out m and b:

w₁ = mz₁ + b
w₂ = mz₂ + b

m = (w₂ - w₁) / (z₂ - z₁)
b = w₁ - mz₁

In this case w = y² and z = x²y

So, m = (y₂² - y₁²) / ( x₂²y₂ - x₁²y₁)

you should be able to take it from there.