Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 6

Topic

Linear Functions

Description

This example demonstrates the conversion of the linear equation -8x - 12y = 25 from standard form to slope-intercept form. The process involves manipulating the equation to solve for y, yielding y = -2/3 x - 25/12. This transformation clearly reveals the slope and y-intercept of the line.

Linear functions are fundamental mathematical concepts that describe straight-line relationships between variables. 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 affects 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, pay attention to how the coefficients change. What does this tell us about the line's slope and where it crosses the y-axis? How might this line compare to those we've seen in previous examples? Can you think of a real-world situation that this equation might represent?"

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