Download 5 – 4 Direct Variation

5 – 4 A: Direct Variation
Homework Review
A line has a slope of 5
and passes through
the points (4,3) and
(2,y). What is the
value of y?
y = -7
Homework Review
A line passes through
the origin and has a
slope of
.
Through which
quadrants does the
line pass?
II and IV
Definitions
Direct variation – linear relationship between
two variables that can be written in the
form y = kx
Constant of variation – the fixed number (k)
in a direct variation (the coefficient)
**This is another expression that means slope or rate of
change.***
Direct Variation
• Will be a straight line when graphed
• ALWAYS passes through the origin (0,0)
Identifying a Direct Variation from
an Equation
Tell whether each equation represents a
direct variation. If so, identify the constant
of variation.
y = 2x
Yes
k=2
Identifying a Direct Variation from
an Equation
Tell whether each equation represents a
direct variation. If so, identify the constant
of variation.
y = 1/3 x
Yes
k = 1/3
Identifying a Direct Variation from
an Equation
Tell whether each equation represents a
direct variation. If so, identify the constant
of variation.
y = - ½x
Yes
k = -½
Identifying a Direct Variation from
an Equation
Tell whether each equation represents a
direct variation. If so, identify the constant
of variation.
y = 2x + 3
No
Identifying a Direct Variation from
an Equation
Tell whether each equation represents a
direct variation. If so, identify the constant
of variation.
y = ½x - 6
No
Identifying a Direct Variation from
an Equation
Tell whether each equation represents a
direct variation. If so, identify the constant
of variation.
2y = x
Identifying a Direct Variation from
an Equation
Tell whether each equation represents a
direct variation. If so, identify the constant
of variation.
2y = x
2 2
y=½x
Yes, this is a direct variation.
½ is the constant of variation.
Identifying a Direct Variation from
an Equation
Tell whether each equation represents a
direct variation. If so, identify the constant
of variation.
y + 1 = 2x
.
Identifying a Direct Variation from
an Equation
Tell whether each equation represents a
direct variation. If so, identify the constant
of variation.
y + 1 = 2x Solve for y.
-1 -1
.
y = 2x – 1
.
This is not in the form y = kx, so this is not a
direct variation.
Work with your partner.
Page 214 (1-4)
Notes:
The graph of a direct variation is a line that
passes through the origin (0 0).
The constant of variation (k) is the slope of
the line.
Does this graph represent a direct
variation?
• Yes, the line passes
through the origin, so
this is a direct
variation.
• What is the slope of
the line (constant of
variation)?
k=1
Does this graph represent a direct
variation?
• Yes, the line passes
through the origin, so
this is a direct
variation.
• What is the constant
of variation?
k = -½
Does this graph represent a direct
variation?
• No, the line does not
pass through the
origin, so this is NOT
a direct variation.
Does this graph represent a direct
variation?
• No, the line does not
pass through the
origin, so this is NOT
a direct variation.
Does this graph represent a direct
variation?
• Yes, the line passes
through the origin, so
this is a direct
variation.
22
20
18
16
14
12
• What is the constant
of variation?
k=2
10
8
6
4
2
y = 2x
0
0 1
2
3
4
5
6
7
8
9 10
Does this graph represent a direct
variation?
• No, this is not a
straight line, so this is
NOT a direct
variation.
Let’ look at:
Page 214 (7-8)
Partner Talk
Page 215 (19-24)
Homework:
Page 214 (10-13, 16-17)