Concepts

● Proportion is an equation stating that two ratios or rates are equivalent. It can be written in two ways: as two equal fractions $\frac{\mathrm{a}}{\mathrm{b}}\mathrm{ = }\frac{\mathrm{c}}{\mathrm{d}}$; or using a colon, a:b = c:d.

● Rate – A ratio that compares two quantities with different kinds of units.

● Rate of change – a rate that describes how one quantity changes in relation to another.

● Constant rate of change – two variables have a constant rate of change if the ratio of one variable to the other is proportional.

Rules

If x and y have a proportional relationship, the constant rate of change is the ratio of y to x.

Rate of change = $\frac{\mathrm{y}}{\mathrm{x}}$

Example

Choose the correct rate of change between the two quantities shown in the table.

$\frac{\mathrm{1\; balloon}}{\mathrm{\$\; 6}}$

$\frac{\mathrm{\$\; 3}}{\mathrm{1\; balloon}}$

$\frac{\mathrm{\$\; 6}}{\mathrm{1\; balloon}}$

Solution

1. Calculate the ratio of y to x.

Rate of change = $\frac{6}{2}$ = 3

2. The rate of change is $\frac{\mathrm{\$\; 3}}{\mathrm{1\; balloon}}$.

Answer: 

$\frac{\mathrm{\$\; 3}}{\mathrm{1\; balloon}}$

Pre-requisite Skills

Simplify Fractions (6.4.4)

Understand Ratios (6.6.1)

Ratios and Fractions (6.6.2)

Ratio Applications (6.6.11)

Unit Rate Applications (6.6.12)

Proportional Relationships Applications (6.6.13)