Lesson Plan: Graphing Linear Functions

Lesson Summary

In this lesson, students will explore different methods for graphing linear functions, strengthening their understanding of how algebraic equations relate to their graphical representations. The lesson covers:

• Graphing linear functions using slope-intercept form, standard form, and plotting points.
• Understanding how slope and y-intercept affect the appearance and behavior of a linear graph.
• Identifying the x-intercept and y-intercept and using them to analyze function behavior.

By the end of this lesson, students will be proficient in graphing linear functions and interpreting their meaning in real-world applications.

Key Vocabulary

• x-intercept: The point where a graph crosses the x-axis, indicating where the output value ($y$) is zero.
• y-intercept: The point where a graph crosses the y-axis, representing the output value when the input ($x$) is zero.
• Slope-Intercept Form: A linear equation expressed as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
• Point-Slope Form: A linear equation written as $y - y_1 = m(x - x_1)$, used to define a line with a known slope passing through a specific point $(x_1, y_1)$.
• Increasing Function: A function where the output value increases as the input value increases, indicated by a positive slope.
• Decreasing Function: A function where the output value decreases as the input value increases, indicated by a negative slope.
• Standard Form: A linear equation presented as $Ax + By = C$, where $A$, $B$, and $C$ are integers, and $A$ is non-negative.

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