Math Example--Linear Function Concepts--The Point-Slope Formula: Example 6

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 -7 passing through the point (-8, -5). Using the formula y - y₁ = m(x - x₁), we substitute the given values to get y - (-5) = -7(x - (-8)). After simplification, the resulting equation is y = -7x - 61.

The point-slope form is a powerful tool in linear algebra, allowing us to derive equations of lines efficiently, even when dealing with negative slopes and coordinates. This collection of examples showcases the formula's versatility by presenting various combinations of slopes and points across different quadrants of the coordinate plane. 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 negative numbers and lines that cross multiple quadrants.

Teacher's Script: Let's examine our sixth example. We have a line with a slope of -7 that passes through the point (-8, -5). Can you recall our point-slope formula? Excellent! 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 coordinates for both x and y. 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, especially when dealing with the double negatives.

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