Defining the Slope of a Line
The slope of a line is a number that measures its steepness and direction. It is often described as 'rise over run,' meaning it quantifies how much the line rises vertically for every unit it moves horizontally. A higher slope value indicates a steeper line.
Section 2: The Slope Formula
The slope, typically represented by the letter 'm', is calculated by dividing the change in the vertical y-coordinates (the rise) by the change in the horizontal x-coordinates (the run) between any two distinct points on the line. The formula is: m = (y2 - y1) / (x2 - x1).
Section 3: A Practical Example
Consider a line passing through the points (2, 3) and (4, 7). Using the formula, the rise (y2 - y1) is 7 - 3 = 4, and the run (x2 - x1) is 4 - 2 = 2. The slope 'm' is 4 / 2 = 2. This means for every 1 unit the line moves to the right, it moves 2 units up.
Section 4: Why Slope is Important
Understanding slope is fundamental in many areas of STEM and daily life. It represents a rate of change, such as speed (change in distance over time) in physics or the growth rate of a population in biology. It is also used in engineering and construction to determine gradients for roads or the pitch of a roof.