Use the guess, check, and revise strategy to solve each exercise.

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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

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

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

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 3-6 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

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

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

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

Example #1 Course 3, Lesson 3-6

Another Example Course 3, Lesson 3-6

Example #2 Course 3, Lesson 3-6

Another Example Course 3, Lesson 3-6

Got it? Course 3, Lesson 3-6

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

Example #3 Course 3, Lesson 3-6

Another Example Course 3, Lesson 3-6

Got it? Course 3, Lesson 3-6

Example #4 Course 3, Lesson 3-6

Another Example Course 3, Lesson 3-6

Got it? Course 3, Lesson 3-6

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

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

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