Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 14

Topic

Linear Functions

Description

This image shows a graph with two points (2, -3) and (5, -6). The example demonstrates how to find the equation of a line passing through these points. The slope is calculated as -1, and the point-slope form is used to derive the equation. The slope formula is used: (y₂ - y₁) / (x₂ - x₁) = (-3 - (-6)) / (2 - 5) = 3 / -3 = -1. Then, using the point-slope form: y - (-3) = -(x - 2), which simplifies to y = -x - 1.

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 case with a negative integer slope. By exploring this situation, students can develop a robust comprehension of how negative slopes affect the equation and appearance of a line on a coordinate plane.

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 finding a line's equation, while also exposing them to working with negative slopes. Such repetition helps solidify their understanding and builds their confidence in tackling similar problems independently.

Teacher's Script: Let's move on to our fourteenth example. Here, we have two points: (2, -3) and (5, -6). As we work through this problem, pay attention to how the negative slope affects our equation. We'll use the same process as before, but notice how the signs change when we simplify our equation. This example will help you understand how negative slopes influence the behavior of linear functions.

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