Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 26

Topic

Linear Functions

Description

A graph with two points (-8, -6) and (4, 2) 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 = 1/4 x - 3. The slope is calculated as (2 + 6) / (4 + 8) = 1/4. Using the point-slope form y - y₁ = m(x - x₁), the equation becomes y + 2 = 1/4(x - 4), which simplifies to y = 1/4 x - 3.

This example demonstrates how to work with fractional slopes 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 fractional slopes is crucial for students to develop a comprehensive grasp of linear functions and their various representations.

Exposure to different scenarios in linear functions, including those with fractional slopes, helps students build confidence in their problem-solving skills. This example provides an opportunity for students to practice manipulating fractions 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 this example, we're working with points that give us a fractional slope. Don't let that intimidate you! We'll use the same process as before, carefully calculating our slope and using the point-slope form. Pay close attention to how we handle the fraction when simplifying our equation. Think about what this fractional slope means for the steepness of our line compared to lines with whole number slopes we've seen before.

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