How can I use what I know about linear relationships to create my own

equations?

For example: I have 100 feet of fencing and want to build a dog run with one side length of 40ft. What

are the dimensions of my dog run?

In this lesson you will learn how to create linear equations

to solve problems by identifying relationships

between important information.

Let’s Review

Linear relationships show a constant rate of change.

+ 2 + 2 + 2 + 2

Let’s Review

Solve linear equations for unknown quantities:

3x + 7 = 25 -7 -73x = 18x = 6

Constant rate of change

A Common MistakeDiving in too quickly before

understanding the relationships between the numbers.

A Common Mistake

Letting the numbers dictate the relationship.

Adding is easier than subtracting, so

I should add!

I see two numbers and a

variable. I should multiply.

Core Lesson

Suppose I have 100 feet of fencing to enclose a rectangular dog run. I will

use the entire side of my house, which is 40ft long, as one of the sides of the

dog run.

How long should the other sides be if I want to make sure that I use all of the

fencing I have?

Core Lesson

100 feet of fencingRectangle

House is 40ft. long

40 ft.

40 ft.

LL40

L+ L100

40 + 2L = 100L = 30 feet

Showing a constant rate of change= linear relationship

In this lesson you have learned how to create linear equations

to solve problems by identifying relationships

between important information.

Guided Practice

Write an equation to model the following problem:The lengths of the sides of a triangle are in a ratio of 3:4:5. The perimeter of the triangle is 30cm. Find the lengths of each of the sides.

Extension Activities

Write word problems on 10 index cards and equations modeling the problems on 10 other index cards. Have your friend do the same with other problems. Trade sets of index cards, and match the equation to the word problem.

Extension Activities

Create equations. Trade with a friend and write word problems to model your friend’s equation.

Quick Quiz

Write an equation to model the following problem: Find four consecutive even integers such that the sum of the first and the third is 92.

Quick Quiz

Write an equation to model the following problem:In the 2008 Olympics, Shelly-Ann Fraser won the 100-meter race with a time of 10.78 seconds. The Olympic record, set in 1988 by Florence Griffith-Joyner, was 10.49 seconds. If these two athletes had run in the same race with their respective times above, by how many meters would Griffith Joyner have won?