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The Slope of a Line: Is It Not All Uphill from Here?

In this subtopic we will define the slope of a line, compare slopes of different lines, and explore one of the most useful forms of an equation of a line, slope-intercept form. By writing equations of lines in slope-intercept form, students can then examine the slopes and determine whether two lines are parallel, perpendicular, or neither.

Important definitions include those for:

• vertical change
• horizontal change
• slope
• positive slope
• negative slope
• slope-intercept form
• parallel lines
• perpendicular lines

In this subtopic, we begin with lecture notes for use by the instructor with students or as an individual student activity. In the lecture notes, we define important terms, compare slopes of various lines, write linear equations in slope intercept form to identify the slope and y-intercept, and determine whether two lines are parallel, perpendicular, or neither. Elements within the lecture notes may be used to assess understanding of the content.

Activity two, Slope of a Line Activity, is designed to use in the classroom and encourages students to become involved in the learning process. At the conclusion of the activity, students should be proficient in visualizing positive and negative slopes of lines.

Activity three, What Does That Slope Mean? Activity, can be used as an in-class group activity or take-home assignment. At the conclusion of the activity, students should be able to recognize the properties of positive, negative, and zero slope. Extensions of the activity can include horizontal and vertical translations.

In the summary, instructors are provided with a Pre-Test and Post-Test of the subtopic. Instructors may choose to use both tests, or only the Post-Test as a final assessment.