Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 2

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of 0.5 and a y-intercept of 3. The method involves three main steps: plotting the y-intercept at (0, 3), 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.

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.

Teacher Script: "Now, let's examine our second example. We have a linear function with a slope of 0.5 and a y-intercept of 3. First, we'll plot our y-intercept at (0, 3). Next, we'll use our slope to find another point. A slope of 0.5 means for every 2 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 less steep than our previous example. Can you explain why?"

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