Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 5

Topic

Linear Functions

Description

This example demonstrates how to graph a linear function with a slope of -4 and a y-intercept of 5. The process involves three key steps: first, plotting the y-intercept at (0, 5); second, using the slope to find another point on the line; and finally, connecting these points to form the line.

Linear functions are fundamental in algebra and provide a foundation for understanding more complex mathematical concepts. This collection of examples helps teach the topic by presenting various scenarios with different slopes and y-intercepts, allowing students to visualize how these parameters affect the graph of a linear function, particularly when dealing with negative slopes.

Providing multiple worked-out examples is crucial for students to fully grasp the concept of graphing linear functions. By seeing a variety of cases, students can recognize patterns, understand the relationship between the equation and its graph, and develop the skills to tackle similar problems independently, especially when confronted with negative slopes.

Teacher Script: "Let's look at our fifth example. We have a linear function with a slope of -4 and a y-intercept of 5. Remember, the y-intercept is where our line crosses the y-axis. So, we'll start by plotting a point at (0, 5). Now, we'll use our slope to find another point. A slope of -4 means for every 1 unit we move right, we go down 4 units. Let's do that from our y-intercept. Finally, we'll connect these points to create our line. Notice how this line slopes downward from left to right. What does the negative slope tell us about the relationship between x and y 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.