1. 5.5 Direct Variation
Pg. 326

2. Algebra 5-2 Slope and Direct Variation
Slope Review
Math Pacing
Harbour

3. Definition: Direct Variation
A Direct Variation is a function in the form …
where k does not equal 0.

4. Definition: Constant of Variation
In the equation (function)
The constant of variation is k, the coefficient of x.

5. An equation is a Direct Variation if:
its graph is a line that passes through zero, or
the equation can be written in the form y = kx.

6. Graphing a Slope with a y-intercept at zero
Remember the formula…

7. Graphing a Slope with a y-intercept at zero
Remember the formula…

8. Slope and Constant of Variation
Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
Slope formula
Simplify.
Answer: k = 2 and m = 2.
Notice that the slope of the graph of y = kx is k.
For a direct variation, the slope and constant of variation are identical. (m = k)
Example 2-1a

9. Slope and Constant of Variation
Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
Slope formula
Simplify.
Answer: k = – 4 and m = – 4.
The ordered pair (0, 0) is a solution of y = kx.
Therefore, the graph of y = kx passes through the origin. You can use this information to graph direct variation equations.
Example 2-1b

10. Slope and Constant of Variation
Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
Answer: constant of variation: 4; slope: 4
The ordered pair (0, 0) is a solution of y = kx.
Therefore, the graph of y = kx passes through the origin. You can use this information to graph direct variation equations.
Example 2-1c

11. Direct Variation with k > 0
Step 1 Write the slope as a ratio.
Step 2 Graph (0, 0).
Step 3 From the point (0, 0), move up 1 unit and right 1 unit. Draw a dot.
Step 4 Draw a line containing the points.
Example 2-2a

12. Direct Variation with k > 0
Example 2-2b

13. Direct Variation with k < 0
Step 1 Write the slope as a ratio.
Step 2 Graph (0, 0).
Step 3 From the point (0, 0), move down 3 units and right 2 units. Draw a dot.
Step 4 Draw a line containing the points.
Example 2-3a

14. Direct Variation with k < 0
Example 2-3b

15. Write and Solve a Direct Variation Equation
Suppose y varies directly as x, and when
Write a direct variation equation that relates x and y.
Find the value of k.
Direct variation formula
Replace y with 9 and x with –3.
Divide each side by –3.
Simplify.
Answer: Therefore,
Example 2-4a

16. Write and Solve a Direct Variation Equation
Use the direct variation equation to find x when
Direct variation equation
Replace y with 15.
Divide each side by –3.
Simplify.
Answer: Therefore, when
Example 2-4c

17. Write and Solve a Direct Variation Equation
Suppose y varies directly as x, and when
a. Write a direct variation equation that relates x and y.
b. Use the direct variation equation to find x when
Example 2-4d

18. Is an Equation a Direct Variation
Is an Equation a Direct Variation? If it is, find the constant of variation.
5x + 2y = 0 Solve for y.
Yes, it’s a direct variation.
Constant of variable, k, is

19. Is an Equation a Direct Variation
Is an Equation a Direct Variation? If it is, find the constant of variation.
5x + 2y = 9 Solve for y.
No, it’s not a direct variation.
It’s not in the form y = kx.

20. Is the table a Direct Variation
Is the table a Direct Variation? If it is, find the constant of variation.

21. Is the table a Direct Variation
Is the table a Direct Variation? If it is, find the constant of variation.

22. Homework
Pg. 329, 2 – 34 even