# ResourceMAP - Properties of Linear Functions - 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. **Properties of Linear Functions**

One reason linear functions are useful is obvious—they describe things that move in

a straight line or grow at a constant rate. The graphs are easy to recognize since

they are straight. Graphed lines have slopes and intercepts. Sometimes, lines have

special relationships to other lines, like being parallel or perpendicular. In this

activity, you explore these properties of lines in real-world settings.

**I. Purpose**

• To review how to identify various properties of lines—intercepts, slope,

points being ‘on’ the line, and lines being parallel or perpendicular

• To interpret those properties in contextual situations

**II. Mathematical Focus**

• Point satisfying a linear equation

• Interpreting slope

• *x*- and *y*-intercepts

• Parallel and perpendicular lines

**III. Tip Sheets**

Three Tip Sheets accompany this module.

• **Calculating Slope:** This Tip Sheet uses three 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.

• **Parallel and Perpendicular Lines:** This Tip Sheet reviews the conditions

under which two lines are either parallel or perpendicular and what tests to

use to determine when two lines are parallel or perpendicular.

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

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