Write an equation in pointslope form and slopeintercept
- Slides: 27
Write an equation in point-slope form and slope-intercept form for each line. 1. passes through (2, 5), slope = – 1 2. passes through (1, 9), slope = 4 3. passes through (3, 6) and (1, 2) 4. Bode is planning a party. The cost for 10 people is $170. The cost for 25 people is $470. Write an equation in point-slope form to represent the cost y of having a party for x people. 5. Write the equation in point-slope form that represents the table of values shown. Course 3, Lesson 3 -7
ANSWERS 1. y – 5 = – 1(x – 5); y = –x + 7 2. y – 9 = 4(x – 1); y = 4 x + 5 3. y – 6 = 2(x – 3); y = 2 x 4. Sample answer: y – 170 = 20(x – 10) 5. y – 3 = 2(x – 1) Course 3, Lesson 3 -7
Expressions and Equations WHY are graphs helpful? Course 3, Lesson 3 -7
Expressions and Equations • 8. EE. 8 Analyze and solve pairs of simultaneous linear equations. • 8. EE. 8 a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. • 8. EE. 8 b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. Course 3, Lesson 3 -7 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 • 8. EE. 8 c 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. 7 Look for and make use of structure. Course 3, Lesson 3 -7 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 To • write and solve a system of equations by graphing • determine if the system has no solution, one solution, or an infinite number of solutions Course 3, Lesson 3 -7
Expressions and Equations • systems of equations Course 3, Lesson 3 -7
Example #1 Course 3, Lesson 3 -7
Expressions and Equations How did what you learned today help you answer the WHY are graphs helpful? Course 3, Lesson 3 -7
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Example #2 Course 3, Lesson 3 -7
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Example #3 Course 3, Lesson 3 -7
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Example #4 Course 3, Lesson 3 -7
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Example #5 Course 3, Lesson 3 -7
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Example #6 Course 3, Lesson 3 -7
Course 3, Lesson 3 -7
Another Example: Course 3, Lesson 3 -7
Got it? Course 3, Lesson 3 -7
Expressions and Equations How did what you learned today help you answer the WHY are graphs helpful? Sample answers: • You can graph a system of equations to find the point of intersection of the lines which is the solution. • You can tell if two lines are parallel which means the system has no solutions. • You can tell when two lines are the same line which means the system has an infinite number of solutions. Course 3, Lesson 3 -7
Equations Ratios and. Expressions Proportionaland Relationships Solve the system y = 2 x + 6 and y = – 4 x – 6 by graphing. Course 3, Lesson 3 -7
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