Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 25

Topic

Linear Functions

Description

A graph with two points (-8, 6) and (-3, -4) marked on a coordinate plane. The slope is calculated using the formula (y₂ - y₁) / (x₂ - x₁), and the equation of the line is derived using the point-slope form. The final equation is y = -2x - 10. The slope is calculated as (-4 - 6) / (-3 - (-8)) = -2. Using the point-slope form y - y₁ = m(x - x₁), the equation becomes y - 6 = -2(x + 8), which simplifies to y = -2x - 10.

This example demonstrates how to work with negative coordinates and a negative slope in linear functions. It reinforces the process of calculating slope and using the point-slope form to derive the equation of a line. Understanding how to handle negative values in both coordinates and slopes is crucial for students to develop a comprehensive grasp of linear functions.

Exposure to various scenarios in linear functions, including those with negative values, helps students build confidence in their problem-solving skills. This example provides an opportunity for students to practice manipulating negative numbers and simplifying equations. Such diverse practice is essential for developing mathematical fluency and preparing students for more advanced concepts in algebra and beyond.

Teacher's Script: In our final example, we're dealing with negative coordinates and a negative slope. Don't let the negatives intimidate you! We'll follow the same steps as before. Pay close attention to how we handle the negative numbers when calculating the slope and simplifying our equation. Notice how our final equation reflects the negative slope. Think about what this means for the graph of the line. How will it compare to lines with positive slopes?

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