(8) Lesson 3.5
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1) The document provides examples of finding the slope and y-intercept of linear equations and using intercepts to graph lines. It also includes word problems that can be represented by systems of linear equations. 2) Interpreting intercepts is discussed. The x-intercept represents the point where the line crosses the x-axis, and the y-intercept is where it crosses the y-axis. 3) Graphs are helpful for interpreting real-world situations represented by linear equations and systems of equations. The intercepts can show the breakpoint values where variables are equal to zero.
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1. List all the factors of 88.
2. List all the prime numbers between 25 and 60.
3. Find the GCF for 16 and 17.
4. Find the LCM for 13 and 39.
5. Write the fraction in simplest form.
6. Multiply. Be sure to simplify the product.
7. Divide. Write the result in simplest form.
8. Add.
9. Perform the indicated operation. Write the result in simplest form. –
10. Perform the indicated operation. Write the result in simplest form. ÷
11. Find the decimal equivalent of rounded to the hundredths place.
12. Write 0.12 as a fraction and simplify.
13. Perform the indicated operation. 8.50 – 1.72
14. Divide.
15. Write 255% as a decimal.
16. Write 0.037 as a percent.
17. Evaluate. 56 ÷ 7 – 28 ÷ 7
18. Evaluate. 9 42
19. Multiply: (-1/4)(8/13)
20. Translate to an algebraic expression: Twice x, plus 5, is the same as -14.
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22. Identify the property that is illustrated by the following statement.
(6 · 13) 10 = 6 · (13 · 10)
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26. Subtract. –17 – 6
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28. Multiply.
29. Divide.
30. Evaluate. (–6)2 – 52
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38. A formula that relates Fahrenheit and Celsius temperature is . If the current temperature is 59°F, what is the Celsius temperature?
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- Mauldin Middle School wants to make $4,740 from yearbook sales. Print yearbooks cost $60 each and digital yearbooks cost $15 each.
- This relationship can be represented by the equation 60x + 15y = 4,740.
- Setting y = 0 in the equation yields an x-intercept of 79, meaning 79 print yearbooks would earn the school $4,740.
- Setting x = 0 yields a y-intercept of 316, meaning 316 digital yearbooks would earn the school $4,740.
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1. The document provides examples of writing numbers in standard form and scientific notation. It also gives examples of performing arithmetic operations such as addition, subtraction, multiplication, and division on numbers expressed in scientific notation.
2. The examples calculate population sizes, planet diameters, and perform other calculations to illustrate how scientific notation makes working with very large and small numbers easier.
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- 1. Course 3, Lesson 3-5 State the slope and the y-intercept for the graph of each equation. 1. y = 2x + 1 2. y = 3x + 2 3. y = –2x + 4.5 4. 3x – y = 4 5. The total price of apples y at an orchard can be calculated with the equation 1.12x + 5 = y, where x is the number of pounds of apples picked. What does the slope represent? 6. What is the equation of the graph at the right?
- 2. Course 3, Lesson 3-5 ANSWERS 1. m = 2; b = 1 2. m = 3; b = 2 3. m = -2; b = 4.5 4. m = 3; b = -4 5. the price of apples per pound 6. 1 2 2 y x
- 3. WHY are graphs helpful? Expressions and Equations Course 3, Lesson 3-5
- 4. • 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. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. Course 3, Lesson 3-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Expressions and Equations
- 5. To find the x- and y- intercept • using the slope intercept form of a linear equation • using the standard form of a linear equation Course 3, Lesson 3-5 Expressions and Equations
- 6. • x-intercept • standard form Course 3, Lesson 3-5 Expressions and Equations
- 7. 1 Need Another Example? 2 3 Step-by-Step Example 1. State the x- and y-intercepts of y = 1.5x – 9. Then use the intercepts to graph the equation. First find the y-intercept. y = 1.5x + (–9) b = –9 Write the equation in the form y = mx + b. To find the x-intercept, let y = 0. 0 = 1.5x – 9 Graph the points (6, 0) and (0, –9) on a coordinate plane. Write the equation. Let y = 0. 9 = 1.5x Addition Property of Equality Division Property of Equality 6 = x Simplify. Then connect the points.
- 8. Answer Need Another Example? State the x- and y-intercept of the function y = x – 2. Then graph the function. x-intercept: 3; y-intercept = –2
- 9. 1 Need Another Example? 2 3 Step-by-Step Example 2. Mauldin Middle School wants to make $4,740 from yearbooks. Print yearbooks x cost $60 and digital yearbooks y cost $15. This can be represented by the equation 60x + 15y = 4,740. To find the x-intercept, let y = 0. To find the y-intercept, let x = 0. 60x + 15y = 4,740 60x + 15(0) = 4,740 60x = 4,740 x = 79 Use the x- and y-intercepts to graph the equation. 60x + 15y = 4,740 60(0) + 15y = 4,740 15y = 4,740 y = 316
- 10. Answer Need Another Example? The drama department sold $1,260 worth of tickets to a play. Student tickets x cost $5 and adult tickets y cost $9. This can be represented by the equation 5x + 9y = 1,260. Use the x- and y-intercepts to graph the equation. The x-intercept of 252 means that if 252 student tickets and 0 adult tickets were sold, the total sales would be $1,260. The y-intercept of 140 means that if 0 student tickets and 140 adult tickets were sold, the total sales would be $1,260.
- 11. 1 Need Another Example? 2 Step-by-Step Example 3. Mauldin Middle School wants to make $4,740 from yearbooks. Print yearbooks x cost $60 and digital yearbooks y cost $15. This can be represented by the equation 60x + 15y = 4,740. The x-intercept is at the point (79, 0). This means they can sell 79 print yearbooks and 0 digital yearbooks to earn $4,740. Interpret the x- and y-intercepts. The y-intercept is at the point (0, 316). This means they can sell 0 print yearbooks and 316 digital yearbooks to earn $4,740.
- 12. Answer Need Another Example? The drama department sold $1,260 worth of tickets to a play. Student tickets x cost $5 and adult tickets y cost $9. This can be represented by the equation 5x + 9y = 1,260. Interpret the intercepts. The x-intercept of 252 means that if 252 student tickets and 0 adult tickets were sold, the total sales would be $1,260. The y-intercept of 140 means that if 0 student tickets and 140 adult tickets were sold, the total sales would be $1,260.
- 13. How did what you learned today help you answer the WHY are graphs helpful? Course 3, Lesson 3-5 Expressions and Equations
- 14. How did what you learned today help you answer the WHY are graphs helpful? Course 3, Lesson 3-5 Expressions and Equations Sample answer: • In a real-world situation, a graph can help you interpret the x- and y-intercepts.
- 15. Find the x- and y-intercepts of the equation −x + 3y = 12 and use the intercepts to graph the function. Ratios and Proportional RelationshipsExpressions and Equations Course 3, Lesson 3-5