Chapter 4.5 direct variation.notebook
October 31, 2016
Bellwork
Solve
1)
2)
3)
Chapter 4.5 Direct Variation
Find the slope of the line
Identify, write and graph direct variation.
4) (­2, 3) and (4, 5)
5) 3x ­ y = 9 Oct 27­8:46 PM
Write an equation that describes the relationship:
x
y
1
­2
2
­4
3
­6
4
­8
Direct Variation: a special type of linear relationship that can be written as y = kx, where k is a nonzero constant.
Oct 27­8:51 PM
Determine if the equation is a direct variation (y = kx). If it is a direct variation, then identify the constant of variation.
1) y = ­3x
2) 2x ­ 3y = 2
3) ­3x + 4y = 0
4) 3x + y = 8
Constant of Variation: nonzero constant k.
Oct 27­8:51 PM
Oct 27­8:55 PM
Determine whether each relationship is a direct variation and explain.
Solve y = kx for k.
y
In a direct variation is equal to the constant of variation. x
Every ordered pair (except when x = 0) will have the same ratio y
of . x
5) x
y
2
6
x
y
1
­2
6)
Oct 27­8:59 PM
4 6
12 18
3
0
7
4
Method 1: Write an equation
Method 2: Find y/x for each ordered pair. Oct 27­9:02 PM
1
Chapter 4.5 direct variation.notebook
Determine whether each relationship is a direct variation and explain.
7) x
y
4
5
8 11
13 19
October 31, 2016
Each ordered pair is a solution of a direct variation. Write the equation of the direct variation. Then graph the equation and show that the slope of the line is equal to the constant variation.
9) (5, 6)
Note: The graph of a direct variation always passes through the origin (0, 0).
10) (16, 2)
8)
x
y
11) ­2 3 5
14 ­21 ­35
Oct 27­9:05 PM
Oct 27­9:12 PM
Writing and solving a direct variation:
Writing and solving a direct variation:
12) The value of y varies directly with x, and y = 3 when x = 9. Find y when x = 21.
13) The value of y varies directly with x, and y = 12 when x = 3. Find y when x = 7.
Method 1: Find the value of k and write an equation
Method 1: Find the value of k and write an equation
Method 2: Use a proportion
14) The value of y varies directly with x, and y = 4 when x = 8. Find y when x = 13.
Method 2: Use a proportion
Oct 27­9:08 PM
Oct 27­9:10 PM
Homework
P. 263­265 #1­37, 41­45 (odds)
Oct 27­9:15 PM
Oct 20­9:22 AM
2