Recognize proportional relationships

A proportional relationship links two quantities so that their ratio, or unit rate, remains constant: one quantity is obtained by multiplying the other by a fixed constant. It can be identified in tables of equivalent ratios, graphs that form a straight line through the origin, and equations of the form $y=kx$ ; a straight-line pattern that does not pass through the origin is not proportional, even if its rate of change is constant.

Detailed Explanation: Recognize proportional relationships

A relationship is proportional when the same number connects the two quantities every time. This number is called the unit rate or constant of proportionality.

To check a table:

Divide each $y$ -value by its matching $x$ -value.
Compare the quotients.
If all the quotients are the same, the relationship is proportional.
Write the rule as $y=kx$ , where $k$ is the constant ratio.

Example: Is the relationship in the table proportional?

$x$	$y$
2	5
4	10
6	15

Step 1: Find each ratio.

\frac{5}{2}=2.5

\frac{10}{4}=2.5

\frac{15}{6}=2.5

Step 2: Compare the ratios.

All three ratios are $2.5$ , so the unit rate stays constant.

Step 3: Write the relationship.

Since $y$ is always $2.5$ times $x$ , the equation is

y=2.5x

Therefore, the relationship is proportional. A proportional relationship can also be shown by a straight line that passes through $(0,0)$ , the origin.

Learn by doing: Recognize proportional relationships

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Slope - Find Equivalent - X,Y Chart to Slope Zero Intercept Form

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Recognize proportional relationships

Detailed Explanation: Recognize proportional relationships

Learn by doing: Recognize proportional relationships

Practice with unlimited practice problems

Practice:

Slope - Find Equivalent - X,Y Chart to Slope Zero Intercept Form