1. Use the guess, check, and revise strategy to solve each exercise.
1. The product of two consecutive odd integers is 3,363. What are the integers?
2. Jorge decided to buy a souvenir keychain for $2.25, a cup for $2.95, or a pen for $1.75 for each of his 9 friends. If he spent $22.05 on these souvenirs and bought at least one of each type of souvenir, how many of each did he buy?
3. A number squared is 729. Find the number.
4. Candace has $2.30 in quarters, dimes, and nickels in her change purse. If she has a total of 19 coins, how many of each coin does she have?
Course 3, Lesson 3-6

2. 4. 6 quarters, 3 dimes, 10 nickels
ANSWERS
1. 57 and 59
2. 3 key chains, 4 cups, 2 pens
3. 27
4. 6 quarters, 3 dimes, 10 nickels
Course 3, Lesson 3-6

3. Expressions and Equations
WHY are graphs helpful?
Course 3, Lesson 3-6

4. Mathematical Practices
Expressions and Equations
Preparation for 8.EE.8c Solve real-world and mathematical problems leading to two linear equations in two variables.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
7 Look for and make use of structure.
Course 3, Lesson Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

5. write equations in point-slope form
Expressions and Equations To
write equations in point-slope form
write equations in slope-intercept form
Course 3, Lesson 3-6

6. Expressions and Equations
point-slope form
Course 3, Lesson 3-6

7. Point-Slope Form of a Linear Equation
Expressions and Equations
Point-Slope Form of a Linear Equation
Words The linear equation
is written in point-slope form, where
is a given point on a nonvertical line and m is the slope of the line.
Symbols
Graph
Course 3, Lesson 3-6

8. Example #1
Course 3, Lesson 3-6

9. Another Example
Course 3, Lesson 3-6

10. Example #2
Course 3, Lesson 3-6

11. Another Example
Course 3, Lesson 3-6

12. Got it?
Course 3, Lesson 3-6

13. Write a Linear Equation
Expressions and Equations
Write a Linear Equation
From Slope and a Point
From Slope and y-intercept
From a Graph
From Two Points
From a Table
Substitute the slope m and the coordinates of the point in
Substitute the slope m and y-intercept b in y = mx + b.
Find the y-intercept b and the slope m from the graph, then substitute the slope and y-intercept in y = mx + b.
Use the coordinates of the points to find the slope. Substitute the slope and coordinates of one of the points in
Use the coordinates of the two points to find the slope, then substitute the slope and coordinates of one of the points in
Course 3, Lesson 3-6

14. Example #3
Course 3, Lesson 3-6

15. Another Example
Course 3, Lesson 3-6

16. Got it?
Course 3, Lesson 3-6

17. Example #4
Course 3, Lesson 3-6

18. Another Example
Course 3, Lesson 3-6

19. Got it?
Course 3, Lesson 3-6

20. How did what you learned today help you answer the
Expressions and Equations
How did what you learned
today help you answer the
WHY are graphs helpful?
Course 3, Lesson 3-6

21. How did what you learned today help you answer the
Expressions and Equations
How did what you learned
today help you answer the
WHY are graphs helpful?
Sample answers:
If you need to write an equation from a graph, you can easily locate the y-intercept.
You can find the slope of the line by counting to find the rise and the run.
Course 3, Lesson 3-6

22. Expressions and Equations
Ratios and Proportional Relationships
What is the equation in point-slope form of the line that passes through (−2, 4) and (3, −1)?
Course 3, Lesson 3-6