Lesson Plan 2.5: The Slope of a Line

Objectives:

Students will be able to interpret line graphs and ordered pairs on a graph.
Students will be able to find ordered pairs that satisfy a given equation.
Students will understand x and y intercepts and how to find them.
Students will be able to find the slope of a line given a pair of points, an equation, or a graph.
Students will understand average rate of change as the real-world interpretation of slope.

MWF: You have four days. Spend the first two days on Equations in Two Variables and one day on each of the remaining two topics below.
MW/TR: You have two days, spread among three class sessions. The first (half) day give the lecture on Equations in Two Variables. Have students finish this up on the second day and start the section on Finding the Slope of a Line. Finish the section on the third day.

Give various ordered pairs, and have students plot the values on the board. To tie in the concept of intercepts, give some ordered pairs that are $x$- and $y$-intercepts.
Give one or two examples of a linear equation in two variables, and solve as a class. Point out that finding the intercepts is the quickest, simplest way to do this.
For example, could use $2x+5y=10$ and $4x+3y=12$
Follow up by graphing the above equation(s) solved.
Ask students what form horizontal and vertical lines have: i.e., $y=c$ and $x=a$ for some constant values $c$ and $a$.
Have students work on problems #1-#5.

Write out definition of slope.
Give various sets of points, and as a class calculate slopes.
Give at least three examples of linear equations, and calculate slopes. It's helpful to include one with positive slope and one with negative slope, and an example of a vertical line, and perhaps a horizontal line.
- $6y-3x=18$
- $3y+4x=15$
- $x+5=11$
- $y-7=-11$
Graph the equations together as a class. This gives opportunity for review of how to solve an equation. (Point out, however, that since we have the slope, we only need find one point the line goes through in order to graph.) Be sure to make a point of labeling the axes, and make sure to point out the differences in positive and negative slope -- i.e., rising from left to right vs. falling, and how to "count" slope on the graph.
Have students work on problems #6-#14.

A large point of confusion for students can be what goes in the numerator vs. the denominator when calculating average rate of change. Be sure to emphasize how you know in lecture, and again as you go over problems as necessary.
Problem 2: Encourage group discussion here before discussing as a class. Interpreting graphs is a useful real-world skill.
Problem 5: If students struggle with this, encourage them to find solutions in order to see what ordered pairs the various lines should cross through.
Problem 12: This ties together a lot of concepts and is good if students finish ahead of time one day.
Problem 19: This is a tricky one for students, especially part (c). Encourage them to plug in values and interpret the ordered pair solutions if they struggle to interpret the 350.