Warm Up #4

HW Check – Inverse Worksheet

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

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

2 8

3 12

5 20

X Y

1 4

2 7

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

-1 -2

3 4

6 7

X Y

-6 -2

3 1

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

3. 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

3. 4x = 8y

4. 7x + 4y = 10

Using Proportions

If we know that y varies directly with x. We can use proportions to find missing information.

Ex. Suppose y varies directly with x, and x = 3 when y = 7. Find x when y = 21.

y1x1

y2x2

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

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.

Class work – Group Work

Direct Variation Worksheet

Turn in when you are done!

Homework

Mid-Chapter Review Sheet

# 4 – 15 Show all work for credit!!