Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11

Topic

Linear Functions

Description

The image shows a coordinate plane with two points (-8, -4) and (-2, -4) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated as zero, indicating a horizontal line. The slope is calculated as (y₂ - y₁) / (x₂ - x₁) = (-4 - (-4)) / (-8 - (-2)) = 0 / -6 = 0. Since the slope is zero, it indicates a horizontal line at y = -4. Using point-slope form, the equation becomes y + 4 = 0, which simplifies to y = -4.

Linear functions and their equations are foundational in algebra, enabling students to model real-world situations. This example demonstrates a special case of linear functions: the horizontal line. By presenting this scenario, students can develop a comprehensive understanding of how 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 and build confidence in their problem-solving abilities.

Teacher's Script: Now, let's look at our eleventh example. We have two points: (-8, -4) and (-2, -4). Notice anything special about these points? That's right, they have the same y-coordinate. This means we're dealing with a horizontal line. Let's work through this example together and see how it affects our slope calculation and final equation. Remember, understanding these special cases is just as important as the standard ones!

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