Where `y prop x`, it can be re-written as `y = kx` where `k` is the constant of proportionality.
If two terms are in direct proportion, the terms may be plotted on a graph. For terms to be in direct proportion, when one term evaluates to zero, then the other term must also equal zero.
The gradient of the graph will give the constant of proportionality, `k`.
`x` and `y` are in direct proportion. When `x = 5, y = 7.5`, and when `x=14, y=21`. What is the constant of proportionality?
The gradient is given by `frac(text(up))(text(along))`
= `frac(9)(13.5)` = `frac(2)(3)`
A straight line is drawn through (2, 8) and (4, 12). Does the straight line represent a direct proportion?
The gradient = `frac(12 - 8)(4 - 2)` = `frac(4)(2)` = 2
Using `y=mx+c` and substituting:
`8 = 2 xx 2 + c`
therefore `c = 4`
Because the line does not cross at (0,0), they are not in direct proportion.
See also Using Proportion