1. Direct Variation
Chapter 5.3

2. Direct Variation in Tables
Hours 1 2 3
Miles 60
120
180
Is it linear?
YES!
A linear function varies directly when both variables are zero at the same time.
The equation of the function will be:
dependent variable = (slope) (independent variable.)
y = 60x

3. Direct Variation in Graphs
The graph of a direct variation function goes through the origin (0, 0).
(0,0)
(0,0)

4. Direct Variation in Equations
Equation: y = mx, where m = slope.
Sometimes we use k instead of m.
“k” stands for a constant number.
Slope also called ‘constant variation’

5. Equations with Direct Variation
Equations that DON’T vary directly
Equations with Direct Variation
What do you notice
about these examples?

6. Finding the Constant Variation
Given an Equation:
Given a Point:
is the constant variation.
Slope from (0,0) to (-4, 3) Remember: the rise (y) goes on top.
(-4, 3)
is the constant variation.
would be the equation.

7. Finding the Missing Coordinate
(1, 3) and (4, y)
If the points vary directly, the x-coordinates must be multiplied by the same thing as the y coordinates.
x: 1 multiplied by __ = 4
y: 3 multiplied by 4 = 12
So, y = 12 4

8. Classwork: You may work individually or with ONE other person.
Is each equation a direct variation?
If it is, what is the constant variation?
1) )
3) )
Keep your paper!

9. Continue working with same person, on same piece of paper.
Find the missing coordinate point.
5) (-1, 2) and (4, y)
6) (-2, 5) and (x, -5)
7) (x, -4) and (-9, -12)
y = -8
x = 2
x = -3

10. Classwork: You may work individually or with ONE other person.
Is each statement true or false? Explain.
8) The graph of a direct variation may pass through the point (0, 3).
9) If you double an x-value of a direct variation, the y-value also doubles.
10) The graph of a direct variation can be a vertical line.

11. Homework: Page 228-229 (1-8 all, 13-15 odds, 25-31 odds)
Quiz on : Next Class Period
Tuesday 11/8 or Wednesday 11/9
*Finding the Slope
*Graphing with a Point and Slope
*Using a statement to create and interpret table and graph.