Math Example--Linear Function Concepts--Linear Functions in Tabular and Graph Form: Example 12

Topic

Linear Functions

Description

This example demonstrates the creation of a table of x-y coordinates and the graphing of the linear function y = -x. The image displays both a graph and a table representing this function. The table includes coordinate pairs (0, 0), (1, -1), (2, -2), (3, -3), and (4, -4), illustrating how the y-value decreases by 1 for each unit increase in x.

Linear functions are a key concept in algebra, representing relationships where the rate of change between variables is constant. This collection of examples helps teach this topic by providing visual representations of various linear functions, allowing students to see how changes in the equation affect the graph and table of values.

Exposure to multiple worked-out examples is essential for students to fully grasp the concept of linear functions. By examining different slopes, including negative slopes and the special case of a slope of -1 with a y-intercept of 0, students can develop a more comprehensive understanding of how these components influence the function's behavior.

Teacher's Script: Let's analyze the function y = -x. What's unique about this function? Notice that it passes through the origin, just like y = x, but it slopes downward. For every increase of 1 in x, y decreases by 1. How does this compare to our previous examples? Can you see how this line forms a symmetric pair with y = x?

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