Lesson 1: Equations and Graphs
Duration of Days: 2
Lesson Objective
Students will be able to verify ordered pair that satisfy an equation and plot the points that do satisfy the equation on the x-y coordinate plane.
How do we verify that an ordered pair satisfies an equation?
Ordered pair; Coordinates (x, y); Graph
NA
Lesson Description: This lesson focuses on the standard form of linear equations (Ax + By = C) and the process of generating a graph from an equation. Students will learn to: Verify if a given ordered pair is a solution to a linear equation in two variables. Generate a table of values (T-chart) by choosing independent values for x and calculating the corresponding dependent values for y. Plot the resulting points to reveal the linear nature of the equation. Recognize that any point falling on the line is a solution, while any point off the line is not.
Purpose: The purpose of Section 6.1 is to establish the equivalence between an algebraic rule and a visual line. It teaches students that an equation isn't just a "problem to solve," but a "relationship to map." By manually creating tables of values, students develop an intuition for how changes in the equation (like changing a coefficient) result in physical changes on the graph. This "point-by-point" construction is the necessary precursor to the faster graphing shortcuts (like Slope-Intercept form) introduced later in the chapter.
Depth of Knowledge (DOK) Level
DOK Level 1 & 2
Level 1 (Recall & Reproduction): Evaluating an equation for a specific x-value and plotting the resulting (x, y) coordinate. Recognizing the standard form of a linear equation.
Level 2 (Skill/Concept): Selecting appropriate x-values to create a readable graph (e.g., choosing multiples of a denominator to avoid fractions). Students must transform the equation if necessary to solve for y and then translate that numerical data into a consistent geometric shape.
Class and online work
Use practice problems 1-4, page 143 to assess students' understanding of the lesson concepts