2.3 - Direct Variation
Direct Variation
A linear function defined by an
equation of the form y = kx,
where k ≠ 0, represents direct
variation.
Constant of Variation
The Slope, k, is constant.
It can be represented at the ratio of
y
k=
x
Identifying Direct Variation from a Table
Determine whether y varies directly with x. If so,
find the constant of variation and write the
equations.
1.
2.
X
Y
X
Y
2
8
1
4
3
12
2
7
5
20
5
16
You Try!!
Determine whether y varies directly with x. If so,
find the constant of variation and write the
equations.
1.
2.
X
Y
X
Y
-1
-2
-6
-2
3
4
3
1
6
7
12
4
Identifying Direct Variation from an Equation
For each function, determine whether y varies
directly with x. If so, find the constant of variation:
1. y = 4x
2. 2y = 3x
1.
y = 2x + 3
You Try!!
Determine whether y varies directly with x. If so, find
the constant of variation.
1. y = x/2
2. 2y – 1 = x
1.
4x = 8y
2. 7x + 4y = 10
Using Proportions
If we know that y varies directly with x. We can use
proportions to find missing information.
y1
x1

y2
x2
Ex. Suppose y varies directly with x, and x = 3 when
y = 7. Find x when y = 21.
You Try! y varies directly with x:
 If y = 25 when x = 15, find x when y = 10
 If y = 30 when x = -3, find y when x = -9
Writing Equations
Write an equation of the direct variation that includes
the point (10, -15).
You Try: Write an equation of the direct variation that
includes the point (-40, 16).
Word Problems
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, and write an equation.
Word Problems
The Height of an object varies directly with the length
of its shadow. A person 6 ft tall casts an 8.5 ft shadow,
while a tree casts a 38 ft shadow. How tall is the tree?
Word Problem
The amount of a persons paycheck p varies directly
with the numbers of hours worked t. For 4o hours of
work, the paycheck is $390. Write an equation for
the relationship between hours worked and pay.
Homework
Pg. 74-75: 2-28 even