Proportionality Math Example 2

Follow the full solution, then compare it with the other examples linked below.

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The table shows:

x = 2, y = 8

;

x = 5, y = 20

;

x = 9, y = 36

. Determine whether

y

is proportional to

x

, and if so write the proportionality equation.

1
Compute the ratio $\dfrac{y}{x}$ for each pair: $\dfrac{8}{2} = 4$ , $\dfrac{20}{5} = 4$ , $\dfrac{36}{9} = 4$ .
2
The ratio is constant at $4$ , so $y$ is directly proportional to $x$ .
3
Proportionality equation: $y = 4x$ .

Answer

Yes,

y \propto x

with constant of proportionality

4

; equation:

y = 4x

Direct proportionality means

\frac{y}{x} = k

(a constant) for all data points. Checking all ratios is the key test. The constant

k

is the constant of proportionality, and the relationship always passes through the origin.

About Proportionality

A relationship where two quantities maintain a constant ratio: doubling one always doubles the other, giving $y = kx$ .

A car travels [formula] miles in [formula] hours at constant speed. How far will it travel in [formu

If [formula] apples cost [formula]3.60[formula]20$ apples cost?

Is the relationship [formula] proportional? Is [formula] proportional? Explain.