Unit 2 Linear Equations and Functions Unit Essential

Unit 2 Linear Equations and Functions

Unit Essential Question: 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? Domain Range

Rate of Change = Slope

Graphing Linear Equations Slope Intercept Form Standard Form Horizontal Vertical

Homework: Have a good weekend!

Bell Work:

Lesson 2. 4 – 2. 6 Parallel/Perpendicular Lines, Standard Form, and Direct Variation

Parallel Lines that never intersect. If two lines never intersect, then they must have the same… SLOPE!!!!!! The lines y = 3 x + 10 and y = 3 x – 2 are parallel!!!

Perpendicular Lines Intersecting lines that form 90 degree angles. Perpendicular lines have the opposite-reciprocal slope. The lines y = 3 x + 4 and y = -1/3 x – 8 are perpendicular.

Standard Form Ax + By = C, where A, B, and C are integers (not fractions or decimals). To graph a linear equation in standard form, find the x and y intercepts. X-intercept: this is when y = 0, so simply plug 0 in for y, and solve for x. Y-intercept: this is when x = 0, so simply plug 0 in for x, and solve for y.

Direct Variation In the form y = kx, where k is the constant of variation. To find an equation in direct variation form, you use a given point to find k. Example: If y varies directly with x, and when x = 12, y = 6, write and graph a direct variation equation.

Homework: Page 102 #’s 20 – 25, 40 – 45 Page 109 #’s 3 – 29 odds

Bell Work: 1) Write the equation of a line in standard form that passes through the point (6, -2) and is perpendicular to the line y = -3 x + 4. 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: How do we graph an absolute value function, and how can we predict translations based upon its equation?

Example:

Examples:

Examples with Transformations:

Homework: Page 127 #’s 3 – 20

Bell Work:

Stretching/Shrinking When the absolute value function is multiplied by a number other than 1, it causes the parent function to: Stretch if the number is greater than 1. Shrink if the number is between 0 and 1.

Transformations: This is when a basic parent function is translated, reflected, stretched or shrunk. Translation: when it is shifted left, right, up, or down. Reflection: when it is reflected across the focal point. (multiplied by a negative) Stretched: when it is vertically pulled (multiplied by a # > 1). Shrunk: when it is vertically smushed (multiplied by a # between 0 and 1.

Examples:

Homework: Page 127 #’s 3 – 20

Bell Work: