Math Example--Coordinate Geometry--Slope Formula: Example 16

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (9, -10) and (-1, -2) on a Cartesian plane. The line crosses quadrants III and IV diagonally. Applying the slope formula, we find that the slope is (-2 - (-10)) / (-1 - 9) = 8 / -10 = -4 / 5.

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 both positive and negative coordinates when calculating slope, resulting in a negative fraction.

By providing multiple examples like this, students can see how the slope formula applies in various scenarios, including those involving points in 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 we're dealing with points in different quadrants and with negative coordinates. When calculating the slope, we need to be careful with the signs. The resulting negative slope (-4/5) tells us that the line is decreasing as we move from left to right. For every 5 units we move horizontally to the right, the line falls by 4 units. How does this slope compare to some of the other slopes we've seen in previous examples?

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