# Lesson 8 Point the Way Solidify Understanding

## Learning Focus

Find patterns that are useful in writing equations for linear functions.

Are there different ways to write the equation of a line?

What does each part of an equation tell us?

## Open Up the Math: Launch, Explore, Discuss

Grandma Billings is making a quilt and piecing together a number of blocks. Zac and Sione are watching and thinking about predicting the number of quilt blocks in this pattern:

Zac said: I noticed that two blocks are being added each time. I thought it would be easier if I had the

Sione said: I also noticed that the pattern was growing by two each time. I saw that Pattern 1 just has

### 1.

What does

### 2.

Are the equations that Zac and Sione wrote equivalent? How do you know?

Marcus joined the conversation and noticed this: I was focusing on the strip of blocks in the middle and looking at Patterns 3 and 4. I think that you could also write

### 3.

Do you agree with Marcus? Are these equations all equivalent to Zac’s equation?

Sione said, “What is going on here? I’m going to look at a table to see if I can see why this is working.” Sione made this table and noticed a pattern in the table and the equations they had written.

Sione said, “I used the pattern I saw in the table to write another equation. This time, it’s

Zac said, “I don’t even need the table. I think

### 4.

Examine the table and compare it to the equations that have been written. Explain how Sione might have been using the table when he found the equation

### 5.

Use Sione’s method to find an equation for each of the tables below.

#### a.

#### b.

#### c.

### 6.

What information do you need to write an equation using this method?

### 7.

Write the equation of the line shown in the graph using this method.

### 8.

Use this method to write the equation of the line with slope

### 9.

Zac has a challenge: “I’ll bet you can’t use the pattern to write the equation of the line through the points

### 10.

Sione is still thinking about the pattern: “I wonder if we could use this pattern to graph lines, thinking of the starting point and using the slope.” Try it with the equation:

Starting point:

Slope:

### 11.

Zac wonders, “What is it about lines that makes all this work?” How would you answer Zac?

## Ready for More?

Grandma Billings has started piecing her quilt together and has created the following growth pattern:

See if you can find at least two equivalent equations to model the number of squares in the pattern.

## Takeaways

Point-slope form comes from the slope formula:

With a little rearranging:

## Vocabulary

- point-slope form of a line
**Bold**terms are new in this lesson.

## Lesson Summary

In this lesson, we learned a new and efficient pattern for writing the equation of a line. The method can be used with a table, a graph, or any two points on the line.

Create a graph and explicit equation for the given information.

### 1.

The first term is

Equation:

### 2.

The first term is

Equation:

Rewrite each expression by combining like terms.