Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 13

Topic

Linear Functions

Description

This example demonstrates how to graph a linear function with a slope of 0 and a y-intercept of 0. The process involves recognizing that this special case results in a horizontal line coinciding with the x-axis. The line passes through the origin (0, 0) and extends infinitely in both directions along the x-axis.

Linear functions are fundamental in algebra and provide a foundation for understanding more complex mathematical concepts. This collection of examples helps teach the topic by presenting various scenarios with different slopes and y-intercepts, allowing students to visualize how these parameters affect the graph of a linear function. This particular example showcases the unique case where both the slope and y-intercept are zero, resulting in a line that coincides with the x-axis.

Providing multiple worked-out examples is crucial for students to fully grasp the concept of graphing linear functions. By seeing a variety of cases, including special ones like this, students can recognize patterns, understand the relationship between the equation and its graph, and develop the skills to tackle similar problems independently. This example, in particular, helps students understand the significance of both slope and y-intercept being zero.

Teacher Script: "Let's look at our final example, which is quite special. We have a linear function with both a slope of 0 and a y-intercept of 0. What do you think this graph will look like? That's right, it's a horizontal line that coincides exactly with the x-axis! This line passes through the origin and extends infinitely in both directions. Can you tell me what this means for the y-value of any point on this line? Exactly, y is always 0 no matter what x is. This is a unique case that shows us how powerful the concepts of slope and y-intercept are in determining the behavior of a linear function."

For a complete collection of math examples related to Linear Functions click on this link: Math Examples: Linear Functions in Slope-Intercept Form Collection.