Warm Up

1. In the expression , the coefficient is

___________________.

2. Solve for :

3. Solve for :

4. Find the range of the function for the domain .

Lesson 56: Identifying, Writing, and Graphing Direct

VariationExpressions and Equations, Functions

Direct Variation

Direct variation: when one variable is expressed as a constant times another variable.

Constant of variation: a constant, , that shows the direct variation between and in the equation

Direct VariationRepresentation Description

Equation ; is a nonzero constant

Graph A line that always passes through the origin

Words “ varies directly with .”“ is directly proportional to .”

Example

Tell whether each equation represents a direct variation. If the equation is a direct variation, find the constant of variation.

a.

b.

c.

d.

Example

Tell whether each set of ordered pairs represents a direct variation.

a.

b.

Example

Write an equation for a direct variation that includes the point .

Example

The number of boys in a class varies directly with the number of girls. One class has 6 girls and 18 boys. How many boys will be in a class with 8 girls?

Example

The volume of a box with a fixed base varies directly with its height. A box with a height of 4 centimeters has a volume of 29 cubic centimeters. Graph this relationship, and then use a graph to estimate the volume of a box that is 3 centimeters tall.

Homework Questions

Correcting Homework

Be kind.

Check the paper in front of you. If there is no work shown, return it to its owner.

If the paper in front of you is not in pencil or black ink, return it to its owner.

If the paper in front of you is not complete, return it to its owner.

Remember you are filling out the score sheet for the person that you are correcting.

Be sure to write “C.B. ____________” with your name on the paper you graded and on the score sheet.

Homework

1st and 2nd hour: Lesson 56 #1-16, 18-19, 24-26, Lesson Practice a-i

3rd hour: Lesson 56 #8-9, 13-16, 19, 24-26, Lesson Practice e-i