Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 4

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of 0.1 and a y-intercept of -4. The method involves three main steps: plotting the y-intercept at (0, -4), using the slope to determine a second point on the line, and connecting these points to create the linear graph.

Linear functions are a fundamental concept in 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.

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 independently.

Teacher Script: "Now, let's examine our fourth example. We have a linear function with a slope of 0.1 and a y-intercept of -4. First, we'll plot our y-intercept at (0, -4). Next, we'll use our slope to find another point. A slope of 0.1 means for every 10 units we move right, we go up 1 unit. Let's apply this from our y-intercept. Finally, we'll draw a line through these points. Notice how this line is much less steep than our previous examples. What does this tell us about the rate of change 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.