Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2

Topic

Linear Functions

Description

This example illustrates the process of finding the equation of a line passing through the points (3, 7) and (9, 1). The slope is calculated as -1 using the formula (y₂ - y₁) / (x₂ - x₁). Employing the point-slope form, y - y₁ = m(x - x₁), the equation is derived as y - 1 = -(x - 9), which simplifies to y = -x + 10.

Linear functions form the foundation of algebraic concepts and have wide-ranging applications in real-world scenarios. This collection of examples serves to reinforce the understanding of linear functions by presenting various cases, including positive and negative slopes, as well as special cases like horizontal and vertical lines. By exploring different situations, students can develop a robust comprehension of determining line equations from given points.

The importance of multiple worked-out examples in mathematics education cannot be overstated. Each example in this collection provides students with an opportunity to practice the steps involved in finding a line's equation, while also exposing them to different scenarios they might encounter. This repetition helps solidify their understanding and builds their confidence in tackling similar problems independently.

Teacher's Script: Let's move on to our second example. Here, we have two points: (3, 7) and (9, 1). Notice how these points are different from our first example. We'll use the same process to find the equation of the line passing through these points. Pay attention to how the slope changes and how that affects our final equation. Remember, each example helps reinforce the concept, so stay engaged!

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