Transcript direct variation

88 Direct Variation
Warm Up
Use the point-slope form of each
equation to identify a point the line
passes through and the slope of the
line.
1. y – 3 = – 1
(x – 9) Point:
Slope:
7
2. y + 2 = 2(x – 5)
Point:
Slope:
3. y – 9 = –2(x + 4) Point:
4. y – 5 = – 1 (x + 7) Point:
Slope:
3
4
Slope:
88 Direct Variation
Learn to recognize direct variation by
graphing tables of data and checking for
constant ratios.
Vocabulary
direct variation
constant of proportionality
88 Direct Variation
A direct variation is a linear function that can
be written as y = kx, where k is a nonzero
constant called the constant of variation.
Reading Math
The constant of variation is also called the
constant of proportionality.
88 Direct Variation
Additional Example 1A: Determining Whether a Data
Set Varies Directly
Determine whether the data set shows direct
variation.
88 Direct Variation
Additional Example 1A Continued
Make a graph that shows the relationship between
Adam’s age and his length. The graph is not linear.
88 Direct Variation
Additional Example 1A Continued
You can also compare ratios to see if a direct
variation occurs.
22 ? 27
3 = 12
81 81 ≠ 264
264
The ratios are not proportional.
The relationship of the data is not a direct
variation.
88 Direct Variation
Additional Example 2A: Finding Equations of Direct
Variation
Find each equation of direct variation, given
that y varies directly with x.
y is 54 when x is 6
y = kx
54 = k  6
y varies directly with x.
Substitute for x and y.
9=k
Solve for k.
y = 9x
Substitute 9 for k in the original
equation.
88 Direct Variation
Additional Example 2B: Finding Equations of Direct
Variation
x is 12 when y is 15
y = kx
15 = k

5=k
4
y =5
4x
y varies directly with x.
12
Substitute for x and y.
Solve for k.
5
Substitute 4 for k in the original
equation.
88 Direct Variation
Lesson Quiz: Part I
Find each equation of direct variation, given
that y varies directly with x.
1. y is 78 when x is 3.
2. x is 45 when y is 5.
3. y is 6 when x is 5.
88 Direct Variation
Lesson Quiz: Part II
4. The table shows the amount of money Bob
makes for different amounts of time he works.
Determine whether there is a direct variation
between the two sets of data. If so, find the
equation of direct variation.
88 Direct Variation
Lesson Quiz for Student Response Systems
1. Identify the equation of direct variation given
that y varies directly with x.
y is 75 when x is 5.
A.
B. y = -15x
C. y = 15x
D.
88 Direct Variation
Lesson Quiz for Student Response Systems
2. Identify the equation of direct variation given
that y varies directly with x.
x is 66 when y is 11.
A. y = 66x
B. y = 6x
C.
D.