Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 9

Topic

Linear Functions

Description

This example demonstrates how to graph a linear function with a slope of 0.25 and a y-intercept of 0. The process involves three key steps: first, plotting the y-intercept at the origin (0, 0); 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 fractional positive slopes and zero y-intercepts.

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 fractional slopes and lines passing through the origin.

Teacher Script: "Let's look at our ninth example. We have a linear function with a slope of 0.25 and a y-intercept of 0. Remember, a y-intercept of 0 means our line passes through the origin. So, we'll start by plotting a point at (0, 0). Now, we'll use our slope to find another point. A slope of 0.25 means for every 4 units we move right, we go up 1 unit. Let's do that from our y-intercept. Finally, we'll connect these points to create our line. Notice how this line rises gradually from left to right. What does this tell us about the rate of change in this function compared to our previous examples with steeper slopes?"

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