how to find the slope of a line

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Lines are everywhere in English, whether you are taking Algebra I, Geometry, or Algebra II. If you know how to find the slope of a line,^[1] many things become clearer to you, like whether two lines are parallel or perpendicular, where they will intersect, and many other concepts. Finding the slope of a line is actually pretty easy. Read on for some easy steps you can take to learn how to find the slope of a line.

Practice Problems

1

Understand the slope formula. Slope is defined as "rise over run."^[2]

1

Get a line of which you want to know the slope. Make sure that the line is straight. You can't find the slope of a line that isn't straight.
2

Pick any two coordinates that the line goes through. Coordinates are the x and y points written as (x, y). It doesn't matter which points you pick, as long as they're different points on the same line.^[3]
3

Pick which point's coordinates are dominant in your equation. It doesn't matter which one you pick, as long as it stays the same throughout the calculation. The dominant coordinates will be x ₁ and y ₁. The other coordinates will be x ₂ and y ₂.
4

Set up the equation using the y-coordinates on top and the x-coordinates on bottom. ^[4]
5

Subtract the two y-coordinates from one another.
6

Subtract the two x-coordinates from one another.
7

Divide the y-coordinate's result with the x-coordinate's result. Reduce the number if at all possible.
8
Double-check to see that your number makes sense.
- Lines that go up from left to right are always positive numbers, even if they're fractions.
- Lines that go down from left to right are always negative numbers, even if they're fractions.

Add New Question

Question

How do I find slope of 2x - 4y = 20?

Re-work the equation until y is isolated on one side. Then note the coefficient of the x term. That's the slope. In this example, we re-work the equation until we isolate y: y = x/2 - 5. The coefficient of x is ½, so the slope of the line is ½.
Question

How do I find the slope of a line y=9?

For all lines where y equals a constant and there is no x, the slope is 0.
Question

How do I use a protractor and trigonometry to find slope of a line?

The slope of a line is a non-angular representation of the angle between the line and a horizontal line such as the x-axis. Use a protractor to measure that angle, and then convert the angle to a decimal or a fraction using a trig table. For example, if a protractor tells you that there is a 45° angle between the line and a horizontal line, a trig table will tell you that the tangent of 45° is 1, which is the line's slope. Most angles do not have such a simple tangent. For instance, a 30° angle has a tangent of 0.577. You could use that as the slope, or you could convert the decimal to a fraction, but in this case it would be a rather unwieldy fraction (577/1000 or 72/125).
Question

How do I find the slope of a function with 3 nonlinear points?

You're describing a curved line. Each point on a curve has its own unique slope, so the curve (or function) as a whole does not have a specific slope.
Question

How do I find the slope when x is 5 and -6, and y is -5 and -4?

The slope is the change in y divided by the change in x. The change in y is (-4) - (-5) = -4 + 5 = +1. The change in x is (-6) - (+5) = -6 - 5 = -11. So the slope is +1 / -11 = -1/11. (A negative slope means the line moves down as it moves from left to right, and this slope is just slightly negative.)
Question

Does it matter which two points I choose?

No. Since the line increases at a constant rate, the ratio of (y2-y1)/(x2-x1) will stay the same.
Question

How can I find the slope of the line passing through the points -7, 8 and 5, -7?

Answer is -5/4. You take 8 as your y2 and -7 as your x2. With the rest following in that order, you will be able to get -15/12 which is equal to -5/4.
Question

How do I find a slope with no points?

You would have to use a protractor and trigonometry.
Question

Can I find the slope of -1?

A straight line with a slope of -1 moves down at a 45° angle as it moves to the right.
Question

How to find a slope of a line when equation of a line is given?

When you are given a slope-intercept form equation, then finding the slope is simple: since the slope-intercept form is y = mx + b, and m = slope, it would simply be the coefficient of x. For example, if the question were, "Find the slope when the equation is y = 5x + 2", the slope would be 5, because that is where the slope goes in a slope-intercept form.

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Example

Given: Line AB.
Coordinates: A - (-2, 0) B - (0, -2)
(y₂-y₁): -2-0=-2; Rise = -2
(x₂-x₁): 0-(-2)=2; Run = 2
Slope of Line AB = (Rise/Run) = -1.

You have found "m" in the Line Formula,^[5] which is: y=mx+b, with "y" being the y-coordinate of any given point, "m" being the slope, "x" being the x-coordinate that corresponds with the y-coordinate of any given point, and "b" being the y-intercept.
Once you choose your dominant point's coordinates do not switch them around or you will get the answer wrong.
You can also look in your school textbook or ask your teacher.

Thanks for submitting a tip for review!

Do not confuse the Slope Formula with any other formula, like: Distance Formula, Equation of a Line or Line Formula, or Midpoint Formula.

Things You'll Need

Graph paper (possibly).
A coordinate plane, or a line with two given coordinates.
The Slope Formula.
Pencil and paper,a ruler, a calculator, or just your mind.
Line(s).
x-coordinates.
y-coordinates.

About This Article

Article SummaryX

To find the slope of a line, pick any two coordinates on the line, and choose one of the points to be the dominant point. Use the equation of rise over run, which is Y2-Y1 divided by X2-X1. Subtract the other y-coordinate from the dominant y-coordinate, and subtract the other x-coordinate from the dominant x-coordinate. Leave the answer in fraction form to get the slope of the line! If you want to learn how to reduce the numbers in your slope, keep reading the article!

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