Math Example--Linear Function Concepts--The Point-Slope Formula: Example 8

Topic

The Point-Slope Form

Description

This example demonstrates the application of the point-slope formula to find the equation of a line with a slope of -2 passing through the point (3, -8). Using the formula y - y₁ = m(x - x₁), we substitute the given values to get y - (-8) = -2(x - 3). After simplification, the resulting equation is y = -2x - 2.

The point-slope form is a fundamental concept in linear algebra, providing an efficient method for deriving equations of lines in various positions on the coordinate plane. This collection of examples showcases the formula's versatility by presenting different combinations of slopes and points, including cases with negative slopes and y-intercepts. Through these examples, students can develop a deeper understanding of how to apply the point-slope form in different scenarios.

Exposure to multiple worked-out examples is crucial for students to fully grasp the point-slope form concept. Each example provides a unique set of values, allowing learners to practice applying the formula and recognizing patterns. This repetition helps reinforce understanding and builds confidence in problem-solving skills, particularly when dealing with lines that cross between quadrants and have negative components.

Teacher's Script: Let's examine our eighth and final example in this set. We have a line with a slope of -2 that passes through the point (3, -8). Can you recall our point-slope formula? Great! It's y - y₁ = m(x - x₁). Let's work together to plug in our known values. Notice how we handle the negative slope and y-coordinate. Now, let's simplify our equation step by step to find the final form of our line. Pay attention to how the signs change as we manipulate the equation, and observe how we end up with a negative slope and y-intercept in our final equation.

For a complete collection of math examples related to the Point-Slope Form click on this link: Math Examples: Point-Slope Form Collection.