Lesson 1: Graphing Linear Functions, Zeroes of Linear Functions, Rate of Change of Linear Functions
Duration of Days: 6
Lesson Objective
Students will be able to identify and calculate the rate of change (slope) and y-intercept (initial value) of a linear relationship from tables, graphs, and equations.
They will apply these skills to graph linear functions in slope-intercept form (y = mx + b) and differentiate between proportional and non-proportional relationships.
How can you determine if a relationship is linear and proportional just by looking at its graph or equation?
What is the relationship between the unit rate of a scenario and the slope of its corresponding graph?
How does the y-intercept (initial value) change the starting point of a line on a coordinate plane?
How can you use similar triangles to prove that the slope remains constant between any two points on a line?
Linear Equation: An equation whose graph is a straight line.
Slope (m):
The constant rate of change; the ratio of the vertical change (rise) to the horizontal change (run).
Y-Intercept (b): The point where the graph crosses the y-axis; the output value when the input is zero.
Unit Rate: A comparison of two different quantities where the second value is one unit.
Proportional Relationship: A linear relationship that passes through the origin (0,0).
Similar Triangles: Triangles used along a line to demonstrate constant slope.
8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.EE.B.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line; derive the equations y = mx and y = mx + b.
Target C (1, 2, 3, 5): Graphing proportional relationships, interpreting unit rate as slope, comparing relationships, and finding linear equations.
Description: Students will move from identifying intercepts and calculating slope to constructing and graphing complete linear equations in slope-intercept form.
Purpose: To establish the "connection between proportional relationships, lines, and linear equations".
DOK Level: Level 2 (Basic Application) for calculating slope and graphing; Level 3 (Strategic Thinking) for comparing different representations and explaining constant slope via similar triangles.
Support (Tier 2/3): Provide Identifying y-intercepts foldables and color-coded Slope Between Two Points organizers to scaffold the calculation process.
Scaffolding: Provide step-by-step guides for plotting the intercept before applying the slope.
Extension: Utilize Similar Triangles to prove the slope formula geometrically.
Exit Tickets