Unit D: Graphing

What is Direct Variation?

Scale factor was studied in the Transformations Chapter in Unit A: Chapter 2 Lesson 1.

When enlarging a photo, each side must be multiplied by the same factor to maintain the proportionality of the picture. If a scale factor of 3 is applied to the small photograph of the horses, each dimension is multiplied by 3 to enlarge the photograph.




Direct variation means that when the x-values increase by an equal amount, then the y-values also increase by an equal amount (which can be different than the increase in the x-values). In other words, each value of x is multiplied by a constant factor to obtain the value of y. The constant factor is called the rate of change.
 
Does the table of values represent direct variation? If so, explain and state the rate of change.

x y
0 0
1 10
2 20
3 30
4 40






Yes, the table of values represents a direct variation relationship. When the x-value increases by 1, the y-value increases by 10.

Each value of x is multiplied by a factor of 10 to produce each y-value.

x y
0 0 0 × 10 = 0
1 10 1 × 10 = 10
2 20 2 × 10 = 20
3 30 3 × 10 = 30
4 40 4 × 10 = 40

The constant factor, or rate of change, is 10.
Does the table of values represent direct variation? If so, explain and state the rate of change.

x y
0 0
1 5
2 9
3 12
4 14







When the x-value increases by 1, the y-value increases by 2, 3, 4, or 5.

x y
0 0
1 5 1 × 5 = 5
2 9 2 × 4.5 = 9
3 12 3 × 4 = 12
4 14 4 × 3.5 = 14

Since the x-values are not multiplied by the same factor to produce the y-values, this set of data does not have a direct variation relationship.