Graphing Equations on the Cartesian Plane: Slope
Ski slopes are an example of real-life mathematical slopesCopyright 2004 Microsoft Corporation, One Microsoft Way, Redmond, WA 98052-6399 USA. All rights reserved.
Students learn about an important characteristic of lines: their slopes. Slope can be determined either in graphical or algebraic form. Slope can also be described as positive, negative, zero or undefined. Students get an explanation of when and how these different types of slope occur. Finally, they learn how slope relates to parallel and perpendicular lines. When two lines are parallel, they have the same slope and when they are perpendicular their slopes are negative reciprocals of one another.
Because many important engineering applications can be better described by a graph of their lines, it is important to understand the characteristics of those lines. One of the most descriptive characteristics of a line is its slope, a key aspect of lines. In the Lesson Closure, students apply the concepts of plotting points and graphing lines to data analysis, as engineers do.
After this lesson, students should be able to:
- Define slope as the ratio of vertical rise to horizontal run.
- Determine the slope of a line given a graph.
- Determine the slope of a line given two points on the line.
- State the formula for slope as:
- Compare slopes of graphs in terms of "more steep," "less steep," etc.
- State what types of lines have slopes of zero or undefined and why.
- Compare slopes of parallel and perpendicular lines.
- Explain how understanding slope will help solve the grand challenge for this unit.