Concepts

Proportion is a statement that two ratios are equal. It can be written in two ways: as two equal fractions ab = cd; or using a colon, a:b = c:d.

Rate is a ratio that compares two quantities with different kinds of units.
Direct Variation is when two variable quantities have a constant ratio.
Constant of Proportionality or constant of variation – the constant ratio. 
The slope is the rate of change between any two points on a line. 

slope = change in y (rise)change in x (run)

Rules

1. In a direct variation equation, the constant rate of change, or slope, is assigned a special variable, k.

2. Direct variation can be represented by the equation: y=kx
Where k≠0

3. When a relationship varies directly, the graph of the function will always go through the origin (0,0). 

Example

Determine if the equation is a direct variation. If so, state the constant of variation.

y=3x+5

Solution

1. Compare to the direct variation equation: 
y=kx  to  y=3x+5  

No, y=3x+5 is not a direct variation

Answer: Not a direct variation. 

Pre-requisite Skills

Rate of change (7.1.7)

Slope (7.1.8)