Chapter 4 – Lines and Linear Equations

Activity 4a – Slopes and Parabolas

This activity has students calculate various slopes of secant lines of a parabola using the slope formula. It then slowly builds the abstraction necessary to deal with the slope of the tangent line in calculus. The intent here is not to teach limits and calculus, but instead to find patterns among the slope calculations and for students to get an appreciation for the process of generalizing the slope to an arbitrary point (x,y).

Slopes and Parabolas

Activity 4b – Slope and Equations of Lines

This activity develops the connection between the slope formula and the Point-Slope form of a line. Most of the math contained within is familiar. The equally important goal is to develop communication skills in dealing with arbitrary points and how to connect a process with the notation.

Slope and Equations of Lines

Activity 4c – Intersections of Lines

This activity finds the formulas from linear algebra and Cramer’s rule, though linear algebra is not discussed here. It is assumed that students have learned processes for finding the intersection of two lines in the xy-plane, most commonly the substitution method and the elimination method. This activity then focuses on the processes used and applies them to a general setting.

Intersection of Lines