Direct proportion refers to the relationship between two variables where their ratio is equal to a constant value.
Given that y is directly proportional to x and that x = 19 when y = 133.
(i) a formula connecting y and x
(ii) the value of y when x = 13
(iii) the value of x when y = 119
y ∝ x
So, y = kx for a constant k.
(i) Given x = 19, when y = 133,
133 = k x 19
k = 133 ÷ 19 = 7
Therefore, the formula is y = 7x
A simpler way to do this is to set it out as a ratio:
Divide both sides by 19 to find the value when x is 1:
1: 133 ÷ 19
y = 7x
(ii) When x = 13, y = 7 x 13 = 91
(iii) When y = 119, x = 119 ÷ 7 = 17
It's useful to have paper and a pencil in order to record your own workings.
These are not the kind of questions you can calculate mentally.
Over to you!