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Unit 2 Linear Equations and Functions Unit Essential Question: ο΅ What are the different ways we can graph a linear equation? Lessons 2.1-2.3 Functions, Slope, and Graphing Lines What is a function? ο΅ Domain ο΅ Range Rate of Change = Slope ο΅π = πβππππ ππ π¦ π£πππ’ππ change in x values Graphing Linear Equations ο΅ Slope Intercept Form ο΅ Standard Form ο΅ Horizontal ο΅ Vertical Homework: ο΅ Have a good weekend! Bell Work: ο΅ 1) Write an equation of a line in standard form that is parallel to the line π¦ = β4π₯ + 2 that passes through the point (-2,1). ο΅ 2) Write the equation of a line in standard form that is perpendicular to the line 4π₯ β 2π¦ = 10 that passes through the point (-4,8) Lesson 2.4 β 2.6 Parallel/Perpendicular Lines, Standard Form, and Direct Variation Parallel Lines ο΅ Lines that never intersect. If two lines never intersect, then they must have the sameβ¦ SLOPE!!!!!! ο΅ The lines y = 3x + 10 and y = 3x β 2 are parallel!!! Perpendicular Lines ο΅ Intersecting lines that form 90 degree angles. Perpendicular lines have the opposite-reciprocal slope. ο΅ The lines y = 3x + 4 and y = -1/3x β 8 are perpendicular. Standard Form ο΅ Ax + By = C, where A, B, and C are integers (not fractions or decimals). ο΅ To graph a linear equation in standard form, find the x and y intercepts. ο΅ X-intercept: this is when y = 0, so simply plug 0 in for y, and solve for x. ο΅ Y-intercept: this is when x = 0, so simply plug 0 in for x, and solve for y. Direct Variation ο΅ In the form y = kx, where k is the constant of variation. ο΅ To find an equation in direct variation form, you use a given point to find k. ο΅ Example: If y varies directly with x, and when x = 12, y = -6, write and graph a direct variation equation. Homework: ο΅ Page 102 #βs 20 β 25, 40 β 45 ο΅ Page 109 #βs 3 β 29 odds Bell Work: ο΅ 1) Write the equation of a line in standard form that passes through the point (6,-2) and is perpendicular to the line y = -3x + 4. ο΅ 2) If y varies directly with x, and when x = 10, y = -30, write and graph a direct variation equation. Lesson 2.7 Absolute Value Functions Lesson Essential Question: ο΅ How do we graph an absolute value function, and how can we predict translations based upon its equation? Example: ο΅ Graph ο΅ This the function: π¦ = |π₯| is the parent function for absolute value functions. Examples: ο΅ Create a table of points, to determine the graph of the given functions. ο΅ Ex: π¦ = π₯ β 2 ο΅ Ex: π¦ = π₯ + 3 ο΅ Ex: π¦ = β2 π₯ + 6 ο΅ Ex: π¦ = 3 π₯ β 2 Examples with Transformations: Homework: ο΅ Page 127 #βs 3 β 20 Bell Work: ο΅ Explain what would happen to each function based upon the changes to the original parent function π¦ = π₯ . ο΅ 1) π¦ = π₯ β 5 ο΅ 2) π¦ = β π₯ + 5 ο΅ 3) π¦ = π₯ + 3 β 2 Stretching/Shrinking ο΅ When the absolute value function is multiplied by a number other than 1, it causes the parent function to: ο΅ Stretch if the number is greater than 1. ο΅ Shrink if the number is between 0 and 1. Transformations: ο΅ This is when a basic parent function is translated, reflected, stretched or shrunk. ο΅ Translation: when it is shifted left, right, up, or down. ο΅ Reflection: when it is reflected across the focal point. (multiplied by a negative) ο΅ Stretched: when it is vertically pulled (multiplied by a # > 1). ο΅ Shrunk: when it is vertically smushed (multiplied by a # between 0 and 1. Examples: Homework: ο΅ Page 127 #βs 3 β 20 Bell Work: ο΅ 1) Write the equation of a line in standard form that passes through the point (-2,6) and is parallel to the line 4x β 2y = 8. ο΅ 2) Find the slope between these two points: (-30,10) and (-6,22) ο΅ 3) If y varies directly with x, and when x = -3, y = - 21, write a direct variation equation and then find y when x = 20. ο΅ 4) Sketch the graph of π¦ = β4 π₯ + 3 + 2