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Algebra 1: Slope, Parallel and Perpendicular Lines, and Linear Equations

This unit focuses on understanding slope, parallel and perpendicular lines, and linear equations in Algebra 1. Topics include slope-intercept and point-slope forms, graphing and writing equations, and direct variation.

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Algebra 1: Slope, Parallel and Perpendicular Lines, and Linear Equations

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  1. Catherine Inman Content Enhancement Final Project EDSP 404 Grade Level: Algebra 1 (9th – 12th grade) SOL: Remember to print: http://www.doe.virginia.gov/VDOE/Instruction/Math/curriculum_framework_2009/algebra1cf.pdf

  2. NAME The Unit Organizer 4 BIGGER PICTURE DATE NEXT UNIT /Experience LAST UNIT /Experience 2 3 CURRENT UNIT CURRENT UNIT 1 is about... 8 UNIT SCHEDULE UNIT MAP 5 Slope Parallel and Perpendicular Lines Slope-Intercept form Point-slope form 6 UNIT SELF-TEST QUESTIONS RELATIONSHIPS UNIT 7 Linear Functions Graphing Relations and Functions Analyzing Linear Equations Solving Linear Inequalities Slope Graphing and Writing Equations using formulas Direct Variation Quiz pp. 256 - 314 By using Slope-intercept By exploring Exploring Activity Point-slope By applying Exploring Activity By applying Quiz Parallel lines Perpendicular lines Quiz Review Unit Test Identify • Describe what is slope? • How would you relate slope to climbing a mountain? • Compare and contrast point-slope and slope-intercept form. • Compare and contrast parallel and perpendicular lines? Solve Graph Manipulate

  3. NAME The Unit Organizer DATE Expanded Unit Map 9 is about... y2 – y1 =m x2 – x1 Slope Parallel and Perpendicular Lines Slope-Intercept form Point-slope form y – y1 = m(x – x1) 10 NEW UNIT SELF-TEST QUESTIONS Linear Functions Rise over run By using Graphing and Writing Equations using formulas By exploring m = m pp. 256 - 314 m = -1/m By applying By applying y = mx + b

  4. Key Topic The FRAME Routine is about… Main idea Main idea Main idea Essential details Essential details Essential details So What? (What’s important to understand about this?) Slope-Intercept Form A linear equation written in the form y = mx+b. Slope y - intercept Variables Change in y’s over change in x’s. What is it? Where the graph crosses the y-axis. Coordinate points Rise over run. Can find it by: y2 – y1 =m x2 – x1 Find y where x = 0 These numbers will vary. Can find only one if given the other. Where in the equation Represented by “m” in the equation y = mx+b. Represented by “b” in the equation y = mx + b. Represented by “x” and “y” in the equation y = mx + b. Is it constant Slope is constant only in a linear equation Always one constant number in a linear equation The coordinate points will change This will help make graphing and solving linear equations easier. Linear equations are used to model things over time such as distance over time or cost over time (speed and inflation).

  5. CONCEPT DIAGRAM À Â CONVEY CONCEPT Á Key Words À Á OFFER OVERALL CONCEPT Â NOTE KEY WORDS Ã CLASSIFY CHARACTERISTICS Always Present Sometimes Present Never Present Ä Examples: Nonexamples: EXPLORE EXAMPLES Å PRACTICE WITH NEW EXAMPLE Æ TIE DOWN A DEFINITION Point – Slope Form Linear Equations Slope Coordinate point Variables x, y Negative numbers Slope Negative numbers Undefined slope Positive numbers (Known) Coordinate point Positive numbers cubic Variables x, y Zero slope Zero slope Undefined slope y - intercept cubic (y-5)=6(x-2) y - intercept (y-5)=6(x-2) y = 5x+3 y = 5x+3 2x + 3y = 10 2x + 3y = 10 (y-7)=2(x-3) 2x + 3y = 10 (y-7)=2(x-3) (y+4)=.5(x-2) (y+4)=.5(x-2) y = 7 (y-2)=1(x+0) (y-2)=1(x+0) y = 7 13,000 13,000 Point – Slope Form is a type of linear equation that uses a known coordinate, slope and variables x and y.

  6. 1 1 1 1 Term Term Term Term 5 5 5 5 LINCing Picture LINCing Picture LINCing Picture LINCing Picture 2 2 2 2 4 4 4 4 Definition Definition Definition Definition LINCing Story LINCing Story LINCing Story LINCing Story 3 3 3 3 Reminding Word Reminding Word Reminding Word Reminding Word Listthe parts Identifya remaining word Note a LINCing story Create a LINCing picture Self-test LINCS Tables Slope Timmy had hope that his grade would change. Ratio of the change in y to the change in x. Hope Direct Variation An equation of the form y = kx where k is a non-zero constant. Sarah had to select the correct form for her paper. Select Constant of variation The number k in equations of the form y = kx. Cindy had to construct the letter k a number of times. Construct Family of graphs A group of graphs or equations of graphs with at least one characteristic in common. The group of farmers had a severe famine that year. Famine

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