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Uploaded byCarol Defreese
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Alg2 lesson 2.2 and 2.3

This document contains information about linear functions and equations including: - The domain and range of relations are specified using set builder notation. - Linear functions are defined as having terms that are either constants or the product of a constant and a single variable to the first power. - Slope-intercept form and standard form of linear equations are explained. - Finding the x- and y- intercepts of a line from its equation is demonstrated. - Slope is defined and calculations of slope between two points is shown. - Lines are classified by their slopes and graphs of equations specifying x or y are given. - Finding parallel and perpendicular lines from a given line is illustrated.

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Name the domain and range for the relation shown in each graphD = {x | x is a real number}D = {x | x is a real number}R = {y | y ≥ 0}R = {y | y ≥ -2}Lesson 2 Contents
In a linear equation, each term is either a constant or the product of a constant and (the first power of) a single variable.Which of these represent linear functions?linearnonlinearlinearnonlinearExample 2-1a
Slope-intercept form y = mx + b f(x) = mx + bm is the slope of the lineb is the y-interceptWhat are the slope and y-intercept of the line ?Slope = 3y-intercept = -9Example 2-1d
The graph of a linear equation is a line.Graph the line y-intercept = -9Slope = 3Slope = ΔyΔxExample 2-1d
Standardform Ax + By = C A, B and C are integers (not fractions!)
A is positive
A and B are not both zero3x + 5y = -2 is in standard formExample 2-1d
Write the equation in standard form. Identify A, B, and C. Ax + By = CSimplified?2 2 2Example 2-3c
Write the equation in standard form. Identify A, B, and C. Ax + By = CSimplified?Example 2-3a
Write the equation in standard form. Identify A, B, and C. Ax + By = C-3 (-3)Simplified?Example 2-3b
Find the x- and y- intercepts of -2x + y – 4 = 0x-intercept-2x + 0 – 4 = 0-2x – 4 = 0-2x = 4x = -2The x-intercept is -2 (-2, 0)y-intercept-2(0) + y – 4 = 00 + y – 4 = 0y – 4 = 0y = 4The y-intercept is 4 (0, 4)Example 2-4b
(0, 4)(–2, 0)Graph -2x + y – 4 = 0x-intercept : –2y-intercept: 4Example 2-4c
Slope m = vertical change Horizontal change m = ΔyΔx m = rise runAny two points on a line can be used to determine its slope.