Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 8

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of -0.25 and a y-intercept of -2. The method involves three main steps: plotting the y-intercept at (0, -2), using the slope to determine a second point on the line, and connecting these points to create the linear graph.

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 fractional negative slopes and negative 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 more complex slope values and negative y-intercepts.

Teacher Script: "Now, let's examine our eighth example. We have a linear function with a slope of -0.25 and a y-intercept of -2. First, we'll plot our y-intercept at (0, -2). Next, we'll use our slope to find another point. A slope of -0.25 means for every 4 units we move right, we go down 1 unit. Let's apply this from our y-intercept. Finally, we'll draw a line through these points. Notice how this line slopes downward from left to right, but less steeply than our previous negative slope example. How does this fractional slope affect the rate of change in our function compared to the previous example?"

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