Find the Slope of a Line

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, 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.

Steps

Slope Formula

  1. Understand the slope formula. Slope is defined as "rise over run."

Solving for Slope

  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. 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 x1 and y1. The other coordinates will be x2 and y2.
  4. Set up the equation using the y-coordinates on top and the x-coordinates on bottom.
  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.



Example

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

Tips

  • You have found "m" in the Line Formula, 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.

Warnings

  • 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.

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