2-3 DIRECT VARIATIONObjective:

To write and interpret direct

variation equations

DIRECT VARIATION

A linear function defined by an equation of the form y = kx where k does not equal zero, represents a direct variation.

As with any line, k is the slope

y = kx

The variables are x and y

The constant is k

For example: If you charge $8 per hour to babysit, how much money will you make?

It depends on how many hours you babysit.- so x is the number of hours

or the independent variable- and y is the amount you will make

or the dependent variable

And k is $8 or the constant

IDENTIFYING THE DIRECT VARIATION FROM A TABLE

y = kx So if we want to solve for k, we need to divide each side

by x

x

kx

x

y

xyk

For the following functions, determine whether y varies directly with x. If so, find the constant of variation

X Y

-6 -2

3 1

12 4

X Y

-1 -2

3 4

6 7

X Y

-9 5

3 -1 2/3

6 3 5/8

X Y

-6 -2

3 1

12 4

3

1

6

2

x

y

3

1

x

y

3

1

12

4

x

y

Since all three are equal, y varies directly with x, and the constant of variation is 1/3

X Y

-1 -2

3 4

6 7

NO

X Y

-9 5

3 -1 2/3

6 3 5/8

NO

FINDING CONSTANT OF VARIATION WHEN GIVEN A DIRECT VARIATION

For a direct variation, y = kx

Substitute the given (x,y) into the equation to find k

Solve for k

EXAMPLEFor the direct variation, find the constant of variation, and then find the value of y if x=-3.

y = -4 when x = 3

y = kx-4 = k(3)-4/3 = k

y = -4/3 xy = (-4/3)(-3)y = 4

ASSIGNMENT

P 74 # 1-22