Last updated on August 5th, 2025
In mathematics, the rise over run formula is used to determine the slope of a line. The slope is the measure of the steepness or incline of a line, typically represented as a ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. In this topic, we will learn the formula for rise over run.
The rise over run formula is essential for calculating the slope of a line. Let’s learn the formula to calculate the rise over run, which is the slope formula.
The rise over run is the slope of a given line, and it is calculated using the formula:
Slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1) Here, (x1, y1) and (x2, y2) are two points on the line.
The rise over run represents how much a line goes up or down (rise) for each unit it goes left or right (run).
A positive slope indicates an upward trend, while a negative slope indicates a downward trend.
The slope is used in various real-world applications such as:
The rise over run formula is crucial for understanding the rate of change between variables. It helps in:
Students often find the slope formula tricky.
Here are some tips to remember it:
Students make errors when calculating slopes. Here are some mistakes and ways to avoid them for better understanding.
Find the slope of a line passing through the points (2, 3) and (6, 11).
The slope is 2
To find the slope, use the formula: (y2 - y1) / (x2 - x1)
Here, (x1, y1) = (2, 3) and (x2, y2) = (6, 11)
Slope = (11 - 3) / (6 - 2) = 8 / 4 = 2
Determine the slope of a line through the points (5, 7) and (10, 15).
The slope is 1.6
To find the slope, use the formula: (y2 - y1) / (x2 - x1)
Here, (x1, y1) = (5, 7) and (x2, y2) = (10, 15)
Slope = (15 - 7) / (10 - 5) = 8 / 5 = 1.6
Find the slope of a line that passes through the points (-3, -1) and (1, 3).
The slope is 1
To find the slope, use the formula: (y2 - y1) / (x2 - x1)
Here, (x1, y1) = (-3, -1) and (x2, y2) = (1, 3)
Slope = (3 - (-1)) / (1 - (-3)) = 4 / 4 = 1
Calculate the slope of a line through the points (0, 5) and (4, 9).
The slope is 1
To find the slope, use the formula: (y2 - y1) / (x2 - x1)
Here, (x1, y1) = (0, 5) and (x2, y2) = (4, 9)
Slope = (9 - 5) / (4 - 0) = 4 / 4 = 1
What is the slope of a line passing through the points (1, 2) and (3, 8)?
The slope is 3
To find the slope, use the formula: (y2 - y1) / (x2 - x1)
Here, (x1, y1) = (1, 2) and (x2, y2) = (3, 8)
Slope = (8 - 2) / (3 - 1) = 6 / 2 = 3
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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