Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 8

Topic

Linear Functions

Description

This example showcases the conversion of the linear equation -7x + 21y = 63 from standard form to slope-intercept form. The process involves rearranging the equation to isolate y, resulting in y = 1/3 x + 3. This transformation clearly reveals the slope and y-intercept of the line.

Linear functions are essential mathematical concepts that describe relationships where one variable changes at a constant rate relative to another. The examples in this collection, showing step-by-step transformations from standard form to slope-intercept form, help students understand how each part of the equation relates to the graph and the underlying relationship.

Exposure to multiple worked-out examples enables students to identify patterns across various representations of linear functions. This reinforces their algebraic skills and enhances their conceptual understanding of linear relationships.

Teacher Script: "As we transform this equation, notice how the coefficients change. What does this tell us about the line's slope and y-intercept? How does this line compare to the ones we've seen in previous examples? Can you think of a real-world scenario where a line with this slope and y-intercept might be useful?"

For a complete collection of math examples related to Linear Functions click on this link: Math Examples: Linear Equations in Standard Form Collection.