Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 24

Topic

Linear Functions

Description

The image shows a graph with two points (-6, -2) and (-3, 4) 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 (4 - (-2)) / (-3 - (-6)) = 2. Using point-slope form: y - 4 = 2(x + 3), which simplifies to y = 2x + 10.

This example showcases a linear function with a positive integer slope, demonstrating how to work with negative coordinates in both the slope calculation and the final equation. It reinforces the importance of careful calculations when dealing with negative numbers. Understanding how to manipulate negative numbers in linear functions is crucial for students as they progress to more advanced mathematical concepts.

Exposure to various types of linear functions, including those with negative coordinates, is essential for building a strong foundation in algebra. This example helps students develop their skills in working with negative numbers and reinforces the connection between graphical representations and algebraic equations. Such practice is invaluable for developing mathematical fluency and problem-solving abilities across different contexts.

Teacher's Script: In this example, we're working with negative coordinates, but we end up with a positive slope. Pay close attention to how we handle the negative numbers when calculating the slope. Notice how our final equation has a positive slope and a positive y-intercept. Think about what this means for the graph of the line. How will it look compared to some of our previous examples?

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