Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 22

Topic

Linear Functions

Description

The image shows a graph with two points (5, 1) and (8, -5) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-5)) / (5 - 8) = -2. Using point-slope form: y - 1 = -2(x - 5), which simplifies to y = -2x + 11.

This example introduces students to working with negative slopes in linear functions. It demonstrates how the sign of the slope affects the direction of the line on the graph. Understanding negative slopes is crucial for students to grasp the full range of linear relationships and their graphical representations. This knowledge is fundamental in various fields, including physics and economics, where negative relationships are common.

Exposure to diverse examples of linear functions helps students develop a comprehensive understanding of the concept. This particular example reinforces the process of finding a line equation while introducing the nuance of negative slopes. Such varied practice enhances students' ability to interpret and manipulate linear functions in different contexts, preparing them for more advanced mathematical concepts.

Teacher's Script: Let's look at an example with a negative slope. Notice how the line slopes downward from left to right. When we calculate the slope, we get a negative integer. Don't let this throw you off! We'll use this negative slope in our point-slope form just like we would a positive one. Pay attention to how the negative slope affects our final equation and think about how this relates to the line's appearance on the graph.

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