Lesson 2: Graphing Linear Functions

How much information is required to define a line? Can two points define a line? Can the slope and a point define a line?

If you know the location of one point on a line and that the slope of the line is -3, how can you locate another point on the line?

F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.

Lesson Description: This lesson focuses on using the parameters of the linear function f(x) = mx + b to construct a graph without the need for a table of values. Students will master: The Starting Point: Identifying the y-intercept (0, b) as the initial point on the graph. The Movement (Slope): Interpreting the slope m as "Rise over Run." Students learn that a positive slope moves up and right, while a negative slope moves down and right. Slope as a Fraction: Converting integer slopes into fractions (e.g., 3= 3/1) to ensure a clear "run" is always available. Graphing Precision: Starting at the y-intercept and using the slope to plot at least two additional points to ensure the line is straight and accurate.
Purpose
The purpose of Section 9.2 is to develop procedural fluency. In future math courses, graphing a line should be a "background task" that takes only a few seconds. By shifting from T-charts to the slope-intercept method, students learn to see the relationship between the algebraic constants (m and b) and their physical manifestation on the grid. This direct link is essential for understanding more complex transformations of functions later in the curriculum.
Depth of Knowledge (DOK) Level
DOK Level 2
Level 2 (Skill/Concept): Students must perform a multi-step mental translation. They have to extract the "starting value" and "rate of change" from an equation and then apply a geometric move (Rise/Run) to plot the line. It requires them to coordinate algebraic signs with directional movement on a 2D plane.

Calculating slope as change in x over change in y, or calculating slope as the change between the coordinates of one point over change between the coordinates of a second point.

Have students plot a line with the given slope that goes through the origin. Then have them move that line up the y-axis until it goes through the desired point.

Use "you try" pg 212 and practice problems to assess students' understanding of the lesson concepts