ResourceMAP - Properties of Linear Functions - 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.

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.