Direct proportion refers to the relationship between two variables where their ratio is equal to a constant value.
Example:
Given that y is directly proportional to x and that x = 19 when y = 133.
Find:
(i) a formula connecting y and x
(ii) the value of y when x = 13
(iii) the value of x when y = 119
Answer:
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
(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!
Some of the questions will require marking before you receive a total score.