Math Example--Linear Function Concepts--Linear Functions in Tabular and Graph Form: Example 8

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 - 8. The image displays both a graph and a table representing this function. The table includes coordinate pairs (0, -8), (1, -7), (2, -6), (3, -5), and (4, -4), illustrating how the y-value increases 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 a slope of 1, y-intercepts, and various combinations of these elements, students can develop a more comprehensive understanding of how these components influence the function's behavior.

Teacher's Script: Let's examine the function y = x - 8. What's unique about this function? Notice that the slope is 1, which means for every increase of 1 in x, y also increases by 1. The y-intercept is -8, which is where our line crosses the y-axis. How does this compare to our previous examples with different slopes?

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.