Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12

Topic

Linear Functions

Description

The image shows a coordinate plane with two points (-5, -8) and (-5, -3) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is undefined, indicating a vertical line. The slope is calculated as (y₂ - y₁) / (x₂ - x₁) = (-3 - (-8)) / (-5 - (-5)) = 5 / 0, which is undefined. Since the slope is undefined, it indicates a vertical line at x = -5. Therefore, the equation of the line is simply x = -5.

Linear functions are a cornerstone of algebraic concepts and have wide-ranging applications in real-world scenarios. This example serves to reinforce the understanding of linear functions by presenting a special case: the vertical line. By exploring this situation, students can develop a robust comprehension of how the relationship between x and y coordinates determines the nature of a line.

The importance of multiple worked-out examples in mathematics education cannot be overstated. This example provides students with an opportunity to practice the steps involved in analyzing a line's equation, while also exposing them to the unique scenario of an undefined slope. Such repetition helps solidify their understanding and builds their confidence in tackling similar problems independently.

Teacher's Script: Let's move on to our twelfth example. Here, we have two points: (-5, -8) and (-5, -3). What do you notice about their x-coordinates? Exactly, they're the same! This is another special case that results in a vertical line. We can't use our usual slope formula here because it would involve dividing by zero. Let's see how we handle this unique situation and what it means for our equation. Pay close attention to how this differs from our previous examples.

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