2.3 Direct Variation
Objective
Write and interpret
direct variation equations.
Title: Old paper (1 of 12)
Check Skills You'll Need:
Solve each equation for y:
1. 12y = 3x
2. 12y = 5x
3. (3/4)y = 15
4. 0.9y = 27x
Tell whether each equation is true:
5.
1
4
=
2
8
6.
Title: Jul 31­8:41 AM (2 of 12)
2
5
=
6
15
7.
9
24
=
12
36
8.
20
24
=
30
36
A DIRECT VARIATION
is a line that always goes through the origin.
y = mx + b
slope
Title: Jul 31­9:02 AM (3 of 12)
y­intercept
What will ALWAYS be
the value of b?
The general form of a direct variation is
y = kx k is the variation constant
How do we find k?
y = kx
y
k= x
Title: Jul 31­9:14 AM (4 of 12)
Divide both sides by x.
For the following function, does y vary directly with x ?
If so, find the constant of variation and write the equation.
x y
2 8
3 12
5 20
k=4
ANSWER
y = 4x
Title: Jul 31­9:36 AM (5 of 12)
For the following function, does y vary directly with x ?
If so, find the constant of variation and write the equation.
x y
1 4
2 7
5 16
y/x is not constant
ANSWER
y does not vary directly with x
Title: Jul 31­9:43 AM (6 of 12)
Can you identify a direct variation from an equation?
For each function, determine whether y varies directly with x.
If so, find the constant of variation.
a. 3y = 2x
y = (2/3)x
k = 2/3
Title: Jul 31­9:47 AM (7 of 12)
b. y = 2x + 3
not direct
variation
A dripping faucet wastes a cup of water if it drips for three minutes. The amount
of water wasted varies directly with the amount of time the faucet drips. Find the
constant of variation k and write an equation to model the direct variation.
Step 1: What is the problem asking us?
water wasted varies directly
with time
Step 2: Define variables.
Let w = # of cups wasted
Let t = time in minutes the faucet drips
Step 3: Write an equation.
w = kt
1 = k(3)
1/3 = k
Substitute 1 for w and 3 for t.
Step 4: Write the direct variation equation with k.
w = (1/3)t
Title: Jul 31­10:25 AM (8 of 12)
y varies directly with x
x = 27 and y = -51
Find x when y = -17
Step 1: Set up a proportion
y1
y2
=
x1
x2
Step 2: Plug in the numbers.
­51
­17
=
x2
27
Step 3: Simplify.
ANSWER
x2 = 9
Title: Jul 31­11:21 AM (9 of 12)
HOMEWORK
p. 74 #1 ­ 22, 52, 55­58
Title: Old paper (10 of 12)
Title: Sep 17­10:29 AM (11 of 12)
Find the equation of the line through the points (­6, 4) and (­3, 6). Write the equation in all three forms
Find the equation of the line perpendicular to 3x ­ 5y = ­7 and through the point (­6, ­2).
Title: Sep 17­12:39 PM (12 of 12)