How to Calculate the Slope of a Line

Lines appear in every corner of Math, whether you’re studying Algebra or Geometry. Once we understand how to calculate the slope of a line, ^{[1] X Source} we will be able to apply it to many cases, such as if you want to know if two lines are parallel or perpendicular, or determine the intersection between those two lines, and so on. Calculating the slope of a straight line is not difficult. This wikiHow teaches you how.

Table of Contents

Formula for calculating slope

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You need to understand the slope formula. The formula for calculating the slope is sometimes called “rise on the run” or m = rise/run. where m is the slope (slope). ^{[2] X Research Source}

Calculate slope

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Select the line for which you want to calculate the slope. This must be a straight line for you to calculate the slope.

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Choose any 2 coordinates lying on the line. Coordinates are pairs of numbers x and y written in the form ( x ; y ). You can choose any point, as long as they lie on the same line and do not overlap. ^{[3] X Research Sources}

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Choose a coordinate as the first point in the equation. You can choose any score, as long as this order is maintained throughout the problem. The coordinates of the first point will be x ₁ and y ₁ . The coordinates of the second point are x ₂ and y ₂ .

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Write an equation with the y coordinates above the numerator and the x coordinates below the denominator. ^{[4] X Research Sources}

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Subtract y ₂ from y ₁ .

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Subtract x ₂ from x ₁ .

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Divide the difference of y ₂ and y ₁ by the difference of x ₂ and x ₁ . Round off decimals if possible.

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Double check your results as follows:

The line going up from left to right has a positive slope, even if it’s a fraction.
The line going down from left to right has a slope that is always negative , even if it’s a fraction.

For example

Given line AB.

Coordinates: A (-2, 0) and B (0, -2)

(y ₂ -y ₁ ): -2-0=-2; increase = -2

(x ₂ -x ₁ ): 0-(-2)=2; run = 2

Slope of line AB = (rise/run) = -2/2 = -1.

Advice

So you have found “m” in the line equation ^{[5] X Research source} : y=mx+b, where “y” is the coordinate of the given point, “m” is the slope (or slope), “x” is the coordinate corresponding to the y coordinate of the given point, “b” is the origin.
After choosing the coordinates of the first point, you must keep this order when calculating because otherwise the result will be wrong.
If you still have questions, you can look at the textbook or ask the teacher.

Warning

Don’t confuse a formula for calculating slope with other knowledge, such as how to calculate distances, equations of lines, or formulas for finding midpoint coordinates.

Things you need

Checkered paper (if any).
Coordinate plane or line with two given coordinates.
Formula for calculating slope.
Pencil, paper, ruler, calculator (or you can do mental math without tools).
Straight line.
Coordinates x.
y coordinate.

Steps