Math Example--Coordinate Geometry--Slope Formula: Example 15

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (4, -5) and (-2, -7) on a Cartesian plane. The line crosses quadrants III and IV. Applying the slope formula, we find that the slope is (-5 - (-7)) / (4 - (-2)) = 2 / 6 = 1 / 3.

The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle points with negative coordinates and in different quadrants when calculating slope.

By providing multiple examples like this, students can see how the slope formula applies in various scenarios, including those involving negative coordinates and different quadrants. This helps reinforce the concept and improves their ability to calculate slopes accurately in more complex situations.

Teacher's Script: Let's examine this example closely. Notice that both points have negative y-coordinates and are in different quadrants. When calculating the slope, we need to be careful with the signs. The resulting positive slope (1/3) tells us that the line is increasing as we move from left to right. For every 3 units we move horizontally to the right, the line rises by 1 unit. How does this slope compare to some of the steeper or more gradual slopes we've seen in previous examples? Can you think of a real-world scenario where a slope of 1/3 might be encountered?

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