Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 19

Topic

Linear Functions

Description

This example illustrates the conversion of the linear equation 12x + 28y = 0 from standard form to slope-intercept form. The solution involves isolating y and dividing by its coefficient, resulting in y = -3/7 x. This process clearly reveals the slope and y-intercept of the line.

Linear functions are crucial mathematical concepts that describe constant-rate 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 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 passing through the origin 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.