Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 15

Topic

Linear Functions

Description

This image shows a graph with two points (3, -4) and (7, -4). The example demonstrates how to find the equation of a horizontal line passing through these points. The slope is calculated as 0, and the point-slope form is used to derive the equation. The slope formula is used: (y₂ - y₁) / (x₂ - x₁) = (-4 - (-4)) / (7 - 3) = 0 / 4 = 0. Then, using the point-slope form: y - (-4) = 0(x - 3), which simplifies to y = -4.

Linear functions are fundamental in algebra and have numerous real-world applications. This example helps teach the concept by providing a scenario with a horizontal line, which is a special case of linear functions. By presenting this case, students can develop a comprehensive understanding of how a zero slope affects the equation and appearance of a line on a coordinate plane.

Exposure to multiple worked-out examples, including special cases like horizontal lines, is crucial for students to fully grasp the concept of linear functions. This example reinforces the steps involved in finding the equation of a line while highlighting the unique situation of a zero slope. Such repetition helps students recognize patterns, build confidence in their problem-solving abilities, and develop a deeper understanding of linear functions and their properties.

Teacher's Script: Now, let's look at our final example in this set. We have two points: (3, -4) and (7, -4). What do you notice about these points? That's right, they have the same y-coordinate. This means we're dealing with a horizontal line, just like in Example 11. Let's work through this example together and compare it to our previous horizontal line example. Remember, recognizing these special cases quickly will help you solve problems more efficiently in the future.

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