ResourceMAP - Linear Equations from Tables, Graphs & Parameters - Teacher Edition

ResourceMAP modules are relatively short and designed for flexible implementation; that is, they can be used in regular classes as well as in special test-preparation settings. Each module contains a set of contextual problems in several formats: multi-part open response, short response, and multiple-choice. Accompanying the problem set are tip sheets that serve several purposes including lists of formulas, calculator instruction, and brief reviews of the module's underlying mathematics. Also provided are teacher notes (the module purpose, the mathematical focus, and implementation commentary), answers to all problems, and (in a few cases) handout masters.

Linear Equations from Tables, Graphs & Parameters

Equations are a useful way to describe certain patterns in tables and graphs.
Equations allow you to decide whether a value matches the rest of the pattern, or to
make predictions based on the pattern. Linear equations are important to
master—they are used by everyone, the patterns are easy to detect, and the
equations are easy to use. In this activity, you examine situations that show a linear
pattern, describe them with an equation, and then use the equation to make
predictions.

I. Purpose
• To formulate linear equations in slope-intercept form from table values,
graphs and parameters that produce linear patterns
• To use the linear equations to make predictions or determine conditions that
correspond to particular situations

II. Mathematical Focus
• Slope formula
• Linear equations in slope-intercept form
• Evaluating equations
• Solving equations

III. Tip Sheets
Three Tip Sheets accompany this module.

• Calculating Slope: This Tip Sheet uses three different scenarios involving
table values to explore how to determine if there is a constant rate-of-change,
and how to calculate the slope when the values show a linear pattern.
In addition, two methods are reviewed for finding the slope of a line from its
graph, and students are reminded to use the general direction of a line to
check for errors in slope calculations.

• Slope-Intercept Equation Form: This Tip Sheet contains methods for
determining an equation of the form y = mx + b from data tables that exhibit
linear patterns and from graphs of lines.

• Fitting a Linear Function with Calculator Regression: If your students
use graphing calculators on exams, you may want to use this sheet. It
discusses the linear regression on TI-83/84 calculators, and the related issues
of making scatter plots and making predictions.