Notes: Lesson 5-2Notes: Lesson 5-2

Objective:Objective:Write and graph direct variation equationsWrite and graph direct variation equations

Vocabulary

Direct Variation:a relationship between x and y where:

if x increases, y also increasesif x increases, y also increasesif x decreases, y also decreasesif x decreases, y also decreases

Direct variation can be described by an equation Direct variation can be described by an equation of the form: of the form: y = kx

k is some number and is called the k is some number and is called the constant of variation

EXAMPLE 1: You have a job making $6.50 per hour.

Let x = # hours you workLet x = # hours you workLet y = total $ you makeLet y = total $ you make

Equation:Equation:y = 6.50xy = 6.50x

This is an example of direct variation….This is an example of direct variation….If your work If your work more hours, you make you make more moneyIf you work If you work fewer hours, you make , you make less money

In this equation, 6.50 is the constant of variation

Graph the equation y = 6.50xMake a table. Pick x’s and use the equation to find y’s.

x

y

x y

0

1

2

3

Don’t pick negative numbers for x…. x represents the number of hours you work!

6.50(0)0

6.50(1)6.50

6.50(2)13.00

6.50(3)19.50

hours

$

0 1 2 3

20 18 16 14 12 10 8 6 4 2

IMPORTANT: the line starts here! Don’t go below (0, 0)!

EXAMPLE 2: The perimeter P of a regular octagon is 8 times the length of the side, s.

Equation:

P = 8s

like y like x

Graph the equation P = 8s

x

y

s P

Make a table. Pick s’s and use the equation to find P’s

0

1

2

3

Don’t pick negative numbers for s…. s represents the number of sides in the octagon!

08(0)

88(1)

168(2)

248(3)0 1 2 3

30 27 24 21 18 15 12 9 6 3

sides

perimeter

For other examples, you will be given an equation For other examples, you will be given an equation such as….such as….

y = 5xy = 5x

y = -2xy = -2x

y = ½ xy = ½ x

We can graph these by making a table, but using We can graph these by making a table, but using the slope is quicker and easierthe slope is quicker and easier

Step 1 Write the slope as a ratio.

Step 2 Graph (0, 0).

Step 3 From the point (0, 0), move up 3 units and right 1 unit. Draw a dot.

Step 4 Draw a line containing the points.

EXAMPLE 3: Graph y = 3x

3 = 3

1

Step 1 Write the slope as a ratio.

Step 2 Graph (0, 0).

Step 3 From the point (0, 0), move up 1 unit and right 1 unit. Draw a dot.

Step 4 Draw a line containing the points.

EXAMPLE 4: Graph y = x

Step 1 Write the slope as a ratio.

Step 2 Graph (0, 0).

Step 3 From the point (0, 0), move down 3 units andright 2 units. Draw a dot.

Step 4 Draw a line containing the points.

EXAMPLE 4:

Assignment:Assignment:Lesson 5-2, page 268Lesson 5-2, page 268

#22, 24, 26, 43-46, 48-51#22, 24, 26, 43-46, 48-51