Proportional Relationship on a Graph

Concept

A proportion is a statement that two ratios are equal. It can be written in two ways: as two equal fractions $\fn_phv \frac{a}{b}=\frac{c}{d}$ ; or using a colon, $\fn_phv a:b=c:d$ .

Rules

Identifying proportional relationships through graphs:
To determine whether two quantities are proportional, graph the quantities on a coordinate plane. If the graph of the two quantities is a straight line through the origin, then the two quantities are proportional.

Identifying proportional relationships through tables:
Write the ratios as fractions and then reduce them.
If the reduced fractions are the same, the ratios are proportional.

Example

Which line represents a proportional relationship?

Solution

1. If the graph is a straight line through the origin, then it represents a proportional relationship.
a. Graph A is a straight line and goes through the origin, so it represents a proportional relationship.
b. Graph B is a straight line but does not go through the origin, so it does not represent a proportional relationship.
Answer: A

Practice Proportional Relationship on a Graph

Practice Problem 1

Which line represents a proportional relationship?

Practice Problem 2

In the following table, are a and b in a proportional relationship?

Practice Problem 3

The ratio of chocolates and ice-creams in the boxes is given in the table below. Is the number of chocolates proportional to the number of ice-creams in each box?