Direct Variation Equations

1
Direct Variation Equations
2
ReviewWhat 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
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 Michaels speed?

• Speed is decreasing

10
4. What does the segment with a positive slope
tell you about Michaels 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

12
(No Transcript)
13
Example 2-1a
Name the constant ofvariation for the
equation.Then find the slope of theline that
passes through thepair of points.
Answer The constant of variation is 2. The
slope is 2.
14
Example 2-1b
Name the constant ofvariation for the
equation.Then find the slope of theline that
passes through thepair of points.
Answer The constant of variation is 4. The
slope is 4.
15
Example 2-1c
Answer constant of variation 4 slope 4
16
Example 2-1d
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 3 slope 3
17

• The constant of variation is the slope

18
(No Transcript)
19
(No Transcript)
20
Example 2-4a
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.
15 k(5) Replace y with 15 and x with 5.
15 k(5) 5 5 Divide each side by 5
3 k Simplify
Equation?
y 3x
21
Example 2-4a
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.
9 k(3) Replace y with 15 and x with 5.
9 k(3) 3 3 Divide each side by 5
3 k Simplify
Equation?
y 3x
22
Example 2-4a
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.
18 k(11) Replace y with 15 and x with 5.
18 k(11) 11 11 Divide each side by 5
18 k Simplify 11
Equation?
y 18x 11
23
Example 2-4a
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.
42 k(7) Replace y with 15 and x with 5.
42 k(7) 7 7 Divide each side by 5
6 k Simplify
Equation?
y 6x
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.
12 k(22) Replace y with 15 and x with 5.
12 k(22) 22 22 Divide each side by 5
6 k Simplify 11
Equation?
y 6 x 11
25
Example 2-5c
Graph the equation.