Math Example--Linear Function Concepts--The Point-Slope Formula: Example 7

Topic

The Point-Slope Form

Description

In this example, we explore finding the equation of a line with a slope of 4 passing through the point (8, -2). Applying the point-slope formula y - y₁ = m(x - x₁), we substitute the given values to obtain y - (-2) = 4(x - 8). After simplification, the final equation of the line is y = 4x - 34.

The point-slope form is a versatile method for deriving linear equations, especially useful when dealing with points in different quadrants of the coordinate plane. This collection of examples illustrates its application across various scenarios, helping students understand how to use the formula with different slopes and points, including those with negative y-coordinates.

Providing multiple worked-out examples is essential for students to internalize the point-slope form concept. Each example offers a unique combination of slope and point coordinates, allowing students to practice the formula's application in different contexts. This approach helps reinforce understanding and builds problem-solving confidence, particularly when dealing with lines that cross between positive and negative y-values.

Teacher's Script: Now, let's move on to our seventh example. Here, we have a line with a slope of 4 that goes through the point (8, -2). Remember our point-slope formula? It's y - y₁ = m(x - x₁). Can you help me identify which values go where in this formula? Excellent! Now, let's work through the steps to simplify our equation and find the final form of our line. Pay special attention to how we handle the negative y-coordinate and how it affects our calculations.

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