Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 12

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of 0 and a y-intercept of -5. The method involves three main steps: plotting the y-intercept at (0, -5), recognizing that a slope of 0 results in a horizontal line, and drawing the line parallel to the x-axis through the y-intercept.

Linear functions are a cornerstone of algebra, providing a visual representation of the relationship between two variables. This collection of examples serves to teach the topic by presenting a range of scenarios with varying slopes and y-intercepts, enabling students to observe how these parameters influence the appearance and behavior of linear graphs, particularly when dealing with zero slopes resulting in horizontal lines at different y-intercepts.

The importance of multiple worked-out examples in mathematics education cannot be overstated. By exposing students to a diverse set of problems, they can identify patterns, internalize the connection between equations and their graphical representations, and develop the confidence to solve similar problems on their own, especially when confronted with special cases like horizontal lines at different positions on the coordinate plane.

Teacher Script: "Now, let's examine our twelfth example. We have a linear function with a slope of 0 and a y-intercept of -5. First, we'll plot our y-intercept at (0, -5). As we learned in our previous example, a slope of 0 means our line will be horizontal. So, we'll draw a straight line parallel to the x-axis passing through our y-intercept. Compare this to our previous example. How is it similar? How is it different? What does the position of this horizontal line tell us about the constant value of y for any x in this 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.