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2010-2011 Algebra 1 Unit 4 PowerPoint

2010-2011 Algebra 1 Unit 4 PowerPoint - Unit 4 Graphing and...

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Unit 4 Graphing and Analyzing Linear Functions Michelle A. O’Malley League Academy of Communication Arts Greenville, South Carolina
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Purpose Statement based on Algebra 1 Learning Goal 4.1 4.1 Seventh and Eighth grade Algebra 1 students will be assessed on their ability to identify if a relationship in tabular or verbal form can be represented by a linear function so that the teacher, parents, instructional coach, and principal can determine if the students have met the required Algebra 1 state standards that are represented in the Graphing and Analyzing Linear Equations Unit (Greenville County School District, 2010)
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Standards for Learning Goal 4.1 EA1.5: Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic) EA3.1: Classify a relationship as being either a function or not a function when given data as a table, set or ordered pairs, or graph.
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Essential Question for Learning Goal 4.1 What does a function look like?
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Learning Goal 4.1 Notes In order to determine whether a relationship is linear, you should focus on the rate of change in the relationship. Linear relationships are characterized by a constant change in one variable associated with a constant change in the other variable. That is, for each unit change in the independent quantity (variable), there is a constant change in the dependent quantity (variable).
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Learning Goal 4.1 Notes A constant rate of change is what makes the line straight .” A constant increase in one variable compared to the other is associated with straight lines having a positive slope. A constant decrease in one variable as compared to the other is associated with straight lines having a negative slope. Some linear functions are proportional and take the form of y=mx. Some linear functions are non-proportional and take the form y=mx + b.
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Learning Goal 4.1 Example 1: Linear or Non Linear? Phil is making a 3 foot by 4 foot banner for the math club. Realizing that the banner is too small, he decides to increase each side. Phil must decide how the new dimensions will affect the cost of the materials. (cost versus area) Non-Linear because the change in area is not constant
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Learning Goal 4.1 Example 2: Linear or Non Linear? A scuba diver is 120 feet below sea level. She knows that to avoid suffering from the bends, she must come up at a rate of 7 feet per minute (depth versus time). Linear because the rate of change is constant
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Learning Goal 4.1 Example 3: Linear or Non Linear? The pattern in the first table is linear : The constant rate of change in the y is zero and the function is y=3. The second pattern is also linear ; the constant rate of change in y is -3 (for a unit change in x) and the function is y=-3x+1.
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