Direct Variation2.4

Big idea…

• 5280ft=1mile. There will always be the same number of feet in a mile, so they are “directly proportional”

Definitions

• Direct Variation: When two things are related by a constant ratio

• Equation:

• The numbers x and y and directly proportional, and k is called the constant of variation.

𝑦=𝑘𝑥

Why is it called DIRECT?

• If x or y increases, so does the other.• If x or y decreases, so does the other.

• They move together in unison.

Example 1

1. Find y if x=3.

2. Find x if y=27.

Example 2

• Find y if x=11

• Find x if y=29

Example 3: You try!

• Find y if x=4

• Find x if y=120

Example 4

• What is the first step in solving for x?

Example 5

Your job pays you $9.50 an hour. 1. Define variables (x and y)

2. Write a direct variation equation.

3. How much will you make if you work 8 hours?

4. How many hours did you work if you make $114?

You try!

You drive at a constant speed of 35 mph.1. Define variables (x and y)

2. Write a direct variation equation.

3. How far will you go if you drive for 4 hours?

4. If you travel 175 miles, how long did you drive?

Homework

• 2.4: problems 3,4,5.