Understanding the Slope Formula
Introduction to Slope
Today we are going to explore the concept of slope in mathematics. Slope is a measure of the steepness or incline of a line. It tells us how much the line rises or falls as we move along it. This is crucial when we’re dealing with graphs in coordinate geometry.
Slope Formula
The slope of a line is usually represented by the letter ‘m’ and is calculated using the following formula:
m = (rise/run) = (y2 – y1) / (x2 – x1)
Here, (x1, y1) and (x2, y2) are any two points on the line.
Examples to Illustrate Slope
Example 1:
Let’s calculate the slope of a line passing through the points (1, 2) and (3, 6).
Using the slope formula:
m = (y2 – y1) / (x2 – x1)
m = (6 – 2) / (3 – 1) = 4 / 2 = 2
Questions Learners Might Have
- What if the line is vertical? – A vertical line does not have a slope, as you would be dividing by zero in the formula, which is undefined.
- Can slope be negative? – Yes, if a line slopes downwards from left to right, its slope is negative.
- What does a slope of zero mean? – A slope of zero means the line is horizontal.
Problems to be Solved During Class
Problem 1: Find the slope of a line passing through the points (4, -2) and (-1, 3).
Answer: m = (3 – (-2)) / (-1 – 4) = 5 / -5 = -1
Problem 2: Calculate the slope of the line that goes through (7, 7) and (7, -1).
Answer: This line is vertical, so the slope is undefined.
Problem 3: Determine the slope of a line that runs through the points (-3, 0) and (-3, 4).
Answer: This is another vertical line, hence the slope is undefined.
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