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

### Author: Gary Froelich

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.

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

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