1. Direct Variation Equations

2. Review What is the slope?

3. Slope = 1/2

4. Slope = -1

5. Slope = 5

6. Slope = Undefined

7. 1. What was the greatest speed that Michael traveled?
65 mph

8. Constant Speed 70 mins - 20 mins = 50 mins
2. What does the horizontal segment of the graph represent? How long does Michael stay at this speed?
Constant Speed
70 mins - 20 mins = 50 mins

9. 3. What does the segment with a negative slope tell you about Michael’s speed?
Speed is decreasing

10. 4. What does the segment with a positive slope tell you about Michael’s speed?
Speed is increasing

11. Vocabulary
Direct Variation Equation – An equation of the form y = kx, where k does not equal zero
Constant of Variation – k in a direct variation equation

13. Answer: The constant of variation is 2. The slope is 2.
Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
Slope formula
Answer: The constant of variation is 2. The slope is 2.
Simplify.
Example 2-1a

14. Answer: The constant of variation is –4. The slope is –4.
Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
Slope formula
Answer: The constant of variation is –4. The slope is –4.
Simplify.
Example 2-1b

15. Answer: constant of variation: 4; slope: 4
Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. a.
Answer: constant of variation: 4; slope: 4
Example 2-1c

16. Answer: constant of variation: –3; slope: –3
Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. b.
Answer: constant of variation: –3; slope: –3
Example 2-1d

17. The constant of variation is the slope

20. Direct variation formula
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.
5. Y = 15 when x = 5
Find the value of k.
Direct variation formula
15 = k(5) Replace y with 15 and x with 5.
15 = k(5)
Divide each side by 5
3 = k Simplify
Equation?
y = 3x
Example 2-4a

21. Direct variation formula
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.
7. Y = 9 when x = 3
Find the value of k.
Direct variation formula
9 = k(3) Replace y with 15 and x with 5.
9= k(3)
Divide each side by 5
3 = k Simplify
Equation?
y = 3x
Example 2-4a

22. Direct variation formula
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.
9. y = 18 when x = 11
Find the value of k.
Direct variation formula
18 = k(11) Replace y with 15 and x with 5.
18= k(11)
Divide each side by 5
18 = k Simplify 11
Equation?
y = 18x 11
Example 2-4a

23. Direct variation formula
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.
11. y = 42 when x = 7
Find the value of k.
Direct variation formula
42 = k(7) Replace y with 15 and x with 5.
42= k(7)
Divide each side by 5
6 = k Simplify
Equation?
y = 6x
Example 2-4a

24. Example 2-4aExample 2-4cExample 2-5b
Y varies directly as x. Find the constant of variation and write an equation for the direct variation.
13. y = 12 when x = 22
Find the value of k.
Direct variation formula
12 = k(22) Replace y with 15 and x with 5.
12= k(22)
Divide each side by 5
6 = k Simplify 11
Equation?
y = 6 x 11
Example 2-4aExample 2-4cExample 2-5b

25. The graph of passes through the origin with a slope of 60.
Graph the equation.
The graph of passes through the origin with a slope of 60.
Answer:
Example 2-5c