CCB Mathematics pages 176 - 183
Use functions to model relationships between quantities.
Use the point-slope form to graph the equation of a line
Use the slope-intercept form to graph the equation of a line
Use the two-point form to graph the equation of a line
There are two ways to graph a linear equation. (1) If two coordinate pairs that lie on the line are known, then the graph of the line can be constructed, or (2) if one coordinate pair that lies on the line and the slope of the line are known, then the graph of the line can be constructed.
|Tier 3||Point-Slope Form
In this lesson, students learn to graph linear equations. To determine student readiness, give students an opportunity to explain a graphical representation of a linear relationship. Project the graphs on pages 170-171 onto the board, or have students examine the graphs in their books. Ask questions about the graphs, using the terms y-intercept, slope, rise, and nm in your questions. Use students’ responses to determine whether students need additional practice using graphs to explain linear relationships before beginning this lesson
Explain to students that the methods for graphing a linear equation on the coordinate plane described in the Key Concept depend on obtaining two coordinate pairs. Those two pairs make it possible to draw a line on which both the points lie. If only one coordinate pair is known, it is possible to use that pair and the slope of the line to find the second coordinate pair.
- Graphing Linear Equations
- Point-Slope Form
- Slope-Intercept Form
Perform Operations: Before reading the text, review the task students completed on the page. Ask them to identify the multiple operations they performed to find a second coordinate pair. Then read the Core Skill sidebar as a class. Ask students to explain the relationship between the following statements: Slope=rise/run; and m=(y_2-y_1)/(x_2-x_1 ).
Interpret Graphs and Functions: The exercise in the Core Skill sidebar gives students an opportunity to apply the point-slope formula to graph a real-world linear relationship. Guide students through the exercise step-by-step, inviting volunteers to create a checklist of important information that they can use to graph and solve the problem.
Retell with Visuals: Invite students to choose one of the forms for finding the equation of a straight line-point-slope form, slope-intercept form, or two-point form. Ask students to explain the form to you in their own words and to include related visuals in their explanations. Offer support if students are struggling to understand these concepts.
Identify Patterns in Data: Have students find a stock market chart in a newspaper or online. Explain to students that the market index or price of a particular stock can change from hour to hour or day to day. Ask students to calculate the slope of line segments that indicate these changes. Remind students to include correct units when calculating the slope, for example, dollars per day.