Math Example--Linear Function Concepts--Linear Functions in Tabular and Graph Form: Example 16

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = -0.5x + 7. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, 7), (1, 6.5), (2, 6), (3, 5.5), and (4, 5), illustrating how the y-value decreases by 0.5 for each unit increase in x.

Linear functions are a fundamental 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 crucial for students to fully grasp the concept of linear functions. By seeing different slopes, including negative fractional slopes, 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: Now, let's analyze the function y = -0.5x + 7. What's different about this function compared to our previous example? Notice the negative fractional slope. For every increase of 1 in x, y decreases by 0.5. How does this affect our graph? The y-intercept is 7, so where does our line cross the y-axis? Can you predict where this line will intersect the x-axis?

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.