Proportionality Math Example 4

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

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Is the relationship

y = 3x + 2

proportional? Is

y = 5x

proportional? Explain.

1
For $y = 3x + 2$ : the ratio $\dfrac{y}{x} = 3 + \dfrac{2}{x}$ , which changes with $x$ . Also the graph does not pass through the origin. Not proportional.
2
For $y = 5x$ : the ratio $\dfrac{y}{x} = 5$ (constant), and the graph passes through the origin. This is proportional, with constant of proportionality $5$ .

Answer

y = 3x + 2

is NOT proportional;

y = 5x

IS proportional.

A proportional relationship has the form

y = kx

with no constant added term, so it always passes through the origin and has a constant ratio

y/x

. Adding a non-zero constant breaks proportionality even though the relationship is still linear.

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

The table shows: [formula]; [formula]; [formula]. Determine whether [formula] is proportional to [fo

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