Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13

Topic

Linear Functions

Description

This image shows a graph with two points (2, -4) and (6, -2) marked. The example demonstrates how to find the equation of a line passing through these points. The slope is calculated as 1/2, and the point-slope form is used to derive the equation of the line. The slope formula is used: (y₂ - y₁) / (x₂ - x₁) = (-2 - (-4)) / (6 - 2) = 2 / 4 = 1/2. Then, using the point-slope form: y - (-2) = (1/2)(x - 6), which simplifies to y = (1/2)x - 5.

Linear functions are fundamental in algebra and have numerous real-world applications. This example helps teach the concept by providing a scenario with a positive fractional slope. By presenting this case, students can develop a comprehensive understanding of how to determine the equation of a line given two points, even when the slope is not a whole number.

Exposure to multiple worked-out examples is crucial for students to fully grasp this concept. This example reinforces the steps involved in finding the equation of a line, while also highlighting the process of working with fractional slopes. 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 thirteenth example. We have two points: (2, -4) and (6, -2). Notice that we're dealing with both positive and negative coordinates this time. We'll use the same process we've been using, but pay close attention to how we handle the fractional slope when deriving our final equation. Remember, practice makes perfect, so let's work through this example together.

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