Math Example--Linear Function Concepts--Linear Functions in Tabular and Graph Form: Example 7

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = x + 7. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 7), (1, 8), (2, 9), (3, 10), and (4, 11), showing how the y-value increases by 1 for each unit increase in x.

Linear functions are essential in algebra as they represent relationships with a constant rate of change between variables. This collection of examples aids in teaching this topic by providing visual representations of various linear functions, enabling students to observe how changes in the equation affect both the graph and the table of values.

Exposing students to multiple worked-out examples is vital for a comprehensive understanding of linear functions. By examining different slopes, including a slope of 1, y-intercepts, and various combinations of these elements, students can develop a deeper insight into how these components influence the function's behavior.

Teacher's Script: Let's examine the function y = x + 7. What's special about the slope in this function? Notice how the y-value increases by exactly 1 for each increase in x. The y-intercept is 7, which means our line crosses the y-axis at (0, 7). How does this function compare to the steeper slopes we've seen in previous examples?

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.