2.3 Direct Variation
“Friendship is born at that moment
when one person says to another,
‘What! You too? I thought I was the
only one.’”
-C. S. Lewis
“A smooth sea never made a skilled mariner.”
-English Proverb
KUDOs
• Know-vocab
Direct variation
slope
Variation constant
Understand how to identify if a relationship
is a direct variation. Understand how to find
the variation constant given two points.
Do-Identify if a function is a direct variation.
Find the variation constant. Apply these
concepts to solve real world situations.
Warm up
1. What form is this
equation in? Graph it.
• Y-3 = -2(x + 4)
2. What form is this
equation in? Graph it.
• 2x – 4y = -8
Direct Variation
Direct Variation is
y = kx
The line passes
through the origin,
and k is the slope.
How can y = kx be
re-written to find k?
Using a Table
Does y vary directly with x in the following
examples?
1.
x
1
4
6
y
3
12
18
2.
x
4
7
8
y
7
9
15
Using Equations
Does y vary directly with x in the following equations?
1. 4y = 24x
2. y =
1x-2
5
Water Conservation
A dripping faucet wastes a cup of water if it drips for 3
minutes. The amount of water wasted varies directly with
the amount of time the faucet drips.
1. DTR (define the relationship)
2. Assign variables
3. Write an equation
4. Substitute the known values
5. Solve for the missing
6. Answer the question in a sentence.
Water Conservation
w=
1
t
3
How long does it take to waste 4.5 cups of water?
Circumference
Circumference varies directly with diameter. C = πd.
What is our constant of variation (k)?
What is the diameter when the circumference is 105 cm.?
Using Proportions
Suppose y varies directly with x, and x = 27 when y = -51. Find x
when y = -17. Then find k.
***Discuss using cross-products!!
2.3 Direct Variation
“Friendship
born
at that
moment
HW:is #
1-19
odd,
23, 24-27,
when one person says to another,
‘What! You too? I thought I was the
only one.’”
33, 34, 46, 47
-C. S. Lewis
“A smooth sea never made a skilled mariner.”
-English Proverb