2.6 Modeling Linear Functions

Lesson Plan 2.6: Modeling Linear Functions

Objectives:

• Students should be able to write equations of lines using both point-slope and slope-intercept forms.
• Students should understand and be able to distinguish parallel and perpendicular lines.
• Students will be able to write linear equations from story problems.

Suggested Lecture Breaks:

• MWF: You have three days. The first day, get through your initial lecture on perpendicular/parallel lines so that they can start Problem 5. The second day, pick up with Problem 6.
• MW/TR: You have 1.5 days. The first day, get through your initial lecture on perpendicular/parallel lines so that they can start Problem 5. The second day, pick up with Problem 6.

Suggested Lecture Notes:

Writing Equations of Lines

• Write definitions of point-slope and slope-intercept form on board; provide examples of each.
• Provide example of points, and practice writing the equation of the line between them. Give both forms. Graph.
• The line through $(5,3)$ and $(-3,1)$.
• Have students work problems 1-4.

Perpendicular and Parallel Lines

• Write both definitions of parallel and perpendicular on the board. Be sure to emphasize the fact that the definition of parallel involves TWO distinct lines... another way to phrase the definition is two lines are parallel when they have the same slope, but different y-intercepts or are distinct vertical lines.
• Give at least one example of each type of equation: parallel, perpendicular, and neither. As a class determine which each is and why. Go back to the definitions and point out the defining characteristics.
• Make the distinction between parallel lines and other pairs of lines with the same slope (which are really just the same line).
• Work through some easy examples where you give them pairs of linear equations and have them determine whether the lines are parallel, perpendicular, or neither. In these examples, point out that everything depends on the slope:
  • To determine if two lines are perpendicular, we need only check the slopes.
  • On the other hand, to determine if two lines are parallel, we need to check both the slopes and the vertical intercepts.
• Have students work on problem 5.
• Give examples of writing equations for parallel and perpendicular lines, such as:
  • The line parallel to the graph of $2x + 8 = y$ passing through the point $(-2, 6)$.
  • The line perpendicular to the graph of $3y+4x=6$ passing through the point $(1,3)$.
• Have students work on problems 6-7.

Writing Equations from Word Problems

• Finally, provide an example of writing a linear equation from a story-problem.
  • Your Netflix account charges a standard \$8.99 per month, and \$1.99 for each extra movie you rent. If $m$ represents the number of movies you rent per month, write a linear equation that represents the total charge, $C$, per month.
  • Then, interpret the ordered pair associated with the equation for $m=10$.
• Have students work on problems 8-10.

Comments on the Handout:

• Problem 8: Be sure to remind students to clearly define any variables not given in the statement.