Linear Equations

Interpret linear models * Define, evaluate, and compare functions * Analyze functions using different representations * Investigate patterns of association in bivariate data * Use functions to model relationships between quantities * Create equations that describe numbers or relationships * Represent and solve equations and inequalities graphically * Build a function that models a relationship between two quantities * Construct and compare linear, quadratic, and exponential models and solve problems * Summarize, represent, and interpret data on two categorical and quantitative variables

Topics

Slope from a Graph and Slope Formula
Linear Equations: Slope-Intercept Form and Standard Form
Graphing Linear Equations (Using Slope-Intercept Form)
x- and y-intercepts
Vertical and Horizontal Lines
Point-Slope Formula (Given a Point and Slope)
Point-Slope Formula (Given Two Points)
Writing Equations of Lines
Parallel and Perpendicular Lines
Scatterplots, Line of Best Fit, and Linear Regression

Prerequisites

Solutions of two-variable equations
Transforming equations
Comparing unit rates
Graphing a function rule
Arithmetic sequences

Goals

Identify relationships in data by using best fit lines from scatterplots
Identify correlation (positive, negative, no correlation)
Compute and interpret the correlation coefficient of a "best fit" line (using technology)
Determine the slope and y-intercept of a set of linear data - by hand and with technology
Identify that the parent function for lines is the line f(x) = x
Identify and graph a line in point-slope form
Identify and graph a line in slope-intercept form
Identify the standard form of a linear function
Identify the x-intercept and y-intercept using the the linear equation in standard form and then graph the line
Given the equation of a line (in any form), find the slope of a parallel line and a perpendicular line.
Use algebra to rewrite linear equations in alternative forms
Write the equation of a line if given: slope & y-intercept; point & slope; two points on the line; or a graph
Write equations of lines involving parallel and perpendicular lines (given a point or intercepts)
Explain the meaning (using appropriate units) of the slope, y-intercept and other points on the line when the line models a real-world relationship
Make predictions based upon given input/output values in a real-world situation
Determine the rate of change over specified time intervals
Model real-world problems that represent linear functions
Determine the slope and y-intercept given the context of real-world situations
Graph a linear inequality with two variables on the coordinate plane
Graph an absolute value function without a table