Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 7

Topic

Linear Functions

Description

This example demonstrates the process of graphing a linear function with a slope of -3 and a y-intercept of -2. The procedure involves three key steps: plotting the y-intercept at (0, -2), using the slope to determine a second point on the line, and connecting these points to form the linear graph.

Linear functions are essential in algebra, providing a straightforward way to visualize relationships between variables. This collection of examples aids in teaching the topic by presenting various scenarios with different slopes and y-intercepts, allowing students to observe how these parameters affect the steepness and position of the line on the coordinate plane, particularly when dealing with negative slopes and negative y-intercepts.

Providing multiple worked-out examples is crucial for students to fully grasp the concept of graphing linear functions. By encountering a variety of cases, students can recognize patterns, understand the relationship between the equation and its graph, and develop the skills to approach similar problems with confidence, especially when working with negative values for both slope and y-intercept.

Teacher Script: "Let's look at our seventh example. We have a linear function with a slope of -3 and a y-intercept of -2. First, we'll plot our y-intercept at (0, -2). Now, we'll use our slope to find another point. A slope of -3 means for every 1 unit we move right, we go down 3 units. Let's do this from our y-intercept. Finally, we'll connect these points to create our line. Notice how steep this line is compared to our previous examples with negative slopes. 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.