How to Find the Slope of an Equation: 3 Easy Methods (2024)

  • Categories
  • Education and Communications
  • Studying
  • Mathematics
  • Algebra

Download Article

Performing common slope calculations so you can solve the toughest math problems, quickly and correctly

Explore this Article

methods

1Finding the Slope of a Linear Equation

2Finding the Slope with Two Points

3Using Differential Calculus to Find the Slope of a Curve

Practice Problems and Answers

+Show 1 more...

-Show less...

Other Sections

Video

Related Articles

References

Article Summary

Co-authored byJake Adams

Last Updated: January 31, 2024Fact Checked

Download Article

The slope of a line is a measure of how fast it is changing. This can be for a straight line -- where the slope tells you exactly how far up (positive slope) or down (negative slope) a line goes while it goes how far across. Slope can also be used for a line tangent to a curve. Or, it can be for a curved line when doing Calculus, where slope is also known as the "derivative" of a function. Either way, think of slope simply as the "rate of change" of a graph: if you make the variable "x" bigger, at what rate does "y" change? That is a way to see slope as a cause and an effect event.

Method 1

Method 1 of 3:

Finding the Slope of a Linear Equation

Download Article

  1. 1

    Use slope to determine how steep, and in what direction (upward or downward), a line goes. Finding the slope of a line is easy, as long as you have or can setup a linear equation. This method works if and only if:[1]

    • There are no exponents on the variables
    • There are only two variables, neither of which are fractions (for example, you would not have How to Find the Slope of an Equation: 3 Easy Methods (5)
    • The equation can be simplified to the form How to Find the Slope of an Equation: 3 Easy Methods (6), where m and b are constants (numbers like 3, 10, -12, How to Find the Slope of an Equation: 3 Easy Methods (7)).[2]
  2. 2

    Find the number in front of the x, usually written as "m," to determine slope. If your equation is already in the right form, How to Find the Slope of an Equation: 3 Easy Methods (8), then simply pick the number in the "m" position (but if there is no number written in front of x then the slope is 1). That is your slope! Note that this number, m, is always multiplied by the variable, in this case an "x." Check the following examples:

    • How to Find the Slope of an Equation: 3 Easy Methods (9)
      • Slope = 2
    • How to Find the Slope of an Equation: 3 Easy Methods (10)
      • Slope = -1
    • How to Find the Slope of an Equation: 3 Easy Methods (11)
      • Slope = How to Find the Slope of an Equation: 3 Easy Methods (12) [3]

    Advertisem*nt

  3. 3

    Reorganize the equation so one variable is isolated if the slope isn't apparent. You can add, subtract, multiply, and more to isolate a variable, usually the "y." Just remember that, whatever you do to one side of the equal sign (like add 3) you must do to the other side as well. Your final goal is an equation similar to How to Find the Slope of an Equation: 3 Easy Methods (14). For example:

    • Find the slope of How to Find the Slope of an Equation: 3 Easy Methods (15)
    • Set to the form How to Find the Slope of an Equation: 3 Easy Methods (16):
      • How to Find the Slope of an Equation: 3 Easy Methods (17)
      • How to Find the Slope of an Equation: 3 Easy Methods (18)
      • How to Find the Slope of an Equation: 3 Easy Methods (19)
      • How to Find the Slope of an Equation: 3 Easy Methods (20)
    • Find the slope:
      • Slope = M = 4[4]
  4. Advertisem*nt

Method 2

Method 2 of 3:

Finding the Slope with Two Points

Download Article

  1. 1

    Use a graph and two points to find slope without the equation handy. If you've got a graph and a line, but no equation, you can still find the slope with ease. All you need are two points on the line, which you plug into the equation How to Find the Slope of an Equation: 3 Easy Methods (23). While finding the slope, keep in mind the following information to help you check if you're on the right track:[5]

    • Positive slopes go higher the further right you go.
    • Negative slopes go lower the further right you go.
    • Bigger slopes are steeper lines. Small slopes are always more gradual.
    • Perfectly horizontal lines have a slope of zero.
    • Perfectly vertical lines do not have a slope at all. Their slope is "undefined."[6]
  2. 2

    Find two points, putting them in simple (x,y) form. Use the graph (or the test question) to find the x and y coordinates of two points on the graph. They can be any two points that the line crosses through. For an example, assume that the line in this method goes through (2,4) and (6,6).[7]

    • In each pair, the x coordinate is the first number, the y coordinate comes after the comma.
    • Each x coordinate on a line has an associated y coordinate.
  3. 3

    Label your points x1, y1, x2, y2, keeping each point with its pair. Continuing our first example, with the points (2,4) and (6,6), label the x and y coordinates of each point. You should end up with:[8]

    • x1: 2
    • y1: 4
    • x2: 6
    • y2: 6[9]
  4. 4

    Plug your points into the "Point-Slope Formula" to get your slope. The following formula is used to find slope using any two points on a straight line: How to Find the Slope of an Equation: 3 Easy Methods (27). Simply plug in your four points and simplify:[10]

    • Original Points: (2,4) and (6,6).
    • Plug into Point Slope:
      • How to Find the Slope of an Equation: 3 Easy Methods (28)
    • Simplify for Final Answer:
      • How to Find the Slope of an Equation: 3 Easy Methods (29) = Slope
  5. 5

    Understand how the Point-Slope Formula works. The slope of a line is “Rise over Run:” how much the line goes up divided by how much the line "runs" to the right. The “rise” of the line is the difference between the y-values (remember, the Y-axis goes up and down), and the “run” of the line is the difference between the x-values (and the X-axis goes left and right).[11]

  6. 6

    Recognize other ways you may be tested to find slope. The equation of the slope is How to Find the Slope of an Equation: 3 Easy Methods (32). This may also be shown using the Greek letter “Δ”, called “delta”, meaning “difference of”. Slope can also be shown as Δy/Δx, meaning "difference of y / difference of x:" this is the same exact question as "find the slope between

  7. Advertisem*nt

Method 3

Method 3 of 3:

Using Differential Calculus to Find the Slope of a Curve

Download Article

  1. 1

    Review how to take a variety of derivatives from common functions. Derivatives give you the rate of change (or slope) at a single point on a line. The line can be curved or straight -- it doesn't matter. Think of it as how much the line is changing at any time, instead of the slope of the entire line. How you take derivatives changes depending on the type of function you have, so review how to take common derivatives before moving on.

    • Review taking derivatives here
    • The most simple derivatives, those for basic polynomial equations, are easy to find using a simple shortcut. This will be used for the rest of the method.
  2. 2

    Understand what questions are asking for a slope using derivatives. You will not always be asked to explicitly find the derivative or slope of a curve. You might also be asked for the "rate of change at point (x,y). You could be asked for an equation for the slope of the graph, which simply means you need to take the derivative. Finally, you may be asked for "the slope of the tangent line at (x,y)." This, once again, just wants the slope of the curve at a specific point, (x,y).

    • To calculate the slope of the tangent line, you need to take the first derivative, and add in the x value into your derivative to get your slope.
    • For this method, consider the question: "What is the slope of the line How to Find the Slope of an Equation: 3 Easy Methods (36) at the point (4,2)?"[12]
    • The derivative is often written as How to Find the Slope of an Equation: 3 Easy Methods (37) or How to Find the Slope of an Equation: 3 Easy Methods (38)
  3. 3

    Take the derivative of your function. You don't even really need you graph, just the function or equation for your graph. For this example, use the function from earlier, How to Find the Slope of an Equation: 3 Easy Methods (40). Following the methods outlined here, take the derivative of this simple function.[13]

    • Derivative: How to Find the Slope of an Equation: 3 Easy Methods (41)
  4. 4

    Plug in your point to the derivative equation to get your slope. The differential of a function will tell you the slope of the function at a given point. In other words, f’(x) is slope of the function at any point (x,f(x)) So, for the practice problem:

    • What is the slope of the line How to Find the Slope of an Equation: 3 Easy Methods (43) at the point (4,2)?
    • Derivative of Equation:
      • How to Find the Slope of an Equation: 3 Easy Methods (44)
    • Plug in Point for x:
      • How to Find the Slope of an Equation: 3 Easy Methods (45)
    • Find the Slope:
    • The slope of the How to Find the Slope of an Equation: 3 Easy Methods (46) at (4,2) is 22.
  5. 5

    Check your point against a graph whenever possible. Know that not all points in calculus will have a slope. Calculus gets into complex equations and difficult graphs, and not all points will have a slope, or even exist on every graph. Whenever possible, use a graphing calculator to check the slope of your graph. If you can't, draw the tangent line using your point and the slope (remember -- "rise over run") and note if it looks like it could be correct.[14]

    • Tangent lines are just lines with the exact same slope as your point on the curve. To draw one, go up (positive) or down (negative) your slope (in the case of the example, 22 points up). Then move over one and draw a point. Connect the dots, (4,2) and (26,3) for your line.
  6. Advertisem*nt

Practice Problems and Answers

Practice Problems and Answers to Find the Slope of an Equation

Community Q&A

Search

Add New Question

  • Question

    What is the slope for the equation y=1?

    How to Find the Slope of an Equation: 3 Easy Methods (49)

    Donagan

    Top Answerer

    The graph of y=1 is a straight, horizontal line, meaning that it does not rise or fall as it moves left or right. Its slope is therefore zero.

    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission.Support wikiHow

    YesNo

    Not Helpful 11Helpful 20

  • Question

    What if the equation is like x+y=0 or x-y=0?

    How to Find the Slope of an Equation: 3 Easy Methods (50)

    Community Answer

    That's no problem. When x+y=0, y=-x. In this case the slope is -1. On the other hand, when x-y=0, y=x. Here the slope is +1.

    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission.Support wikiHow

    YesNo

    Not Helpful 6Helpful 18

  • Question

    What's the difference between a slope = 0 and slope = undefined?

    How to Find the Slope of an Equation: 3 Easy Methods (51)

    Donagan

    Top Answerer

    A zero slope is a horizontal line (parallel to the x-axis), and an undefined slope is a vertical line (parallel to the y-axis).

    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission.Support wikiHow

    YesNo

    Not Helpful 12Helpful 12

See more answers

Ask a Question

200 characters left

Include your email address to get a message when this question is answered.

Submit

      Advertisem*nt

      Video

      Submit a Tip

      All tip submissions are carefully reviewed before being published

      Submit

      Thanks for submitting a tip for review!

      You Might Also Like

      How toFind the Equation of a LineHow to Calculate the Slope of a Line
      How toFind the Equation of a Tangent LineHow to Use the Slope Intercept Form (In Algebra)How toCalculate Slope and Intercepts of a LineHow toFind the Maximum or Minimum Value of a Quadratic Function EasilyHow toFactor a Cubic PolynomialHow toLearn AlgebraHow toSolve a Cubic EquationHow toSolve for XHow toAlgebraically Find the Intersection of Two LinesHow toCalculate FrequencyHow to Solve a Quadratic Equation: A Step-by-Step Guide

      Advertisem*nt

      More References (5)

      About This Article

      How to Find the Slope of an Equation: 3 Easy Methods (66)

      Co-authored by:

      Jake Adams

      Academic Tutor & Test Prep Specialist

      This article was co-authored by Jake Adams. Jake Adams is an academic tutor and the owner of Simplifi EDU, a Santa Monica, California based online tutoring business offering learning resources and online tutors for academic subjects K-College, SAT & ACT prep, and college admissions applications. With over 14 years of professional tutoring experience, Jake is dedicated to providing his clients the very best online tutoring experience and access to a network of excellent undergraduate and graduate-level tutors from top colleges all over the nation. Jake holds a BS in International Business and Marketing from Pepperdine University. This article has been viewed 603,446 times.

      13 votes - 68%

      Co-authors: 20

      Updated: January 31, 2024

      Views:603,446

      Categories: Algebra

      Article SummaryX

      To find the slope of a linear equation, start by rearranging the given equation into slope-intercept form, which is y = mx + b. In slope-intercept form, "m" is the slope and "b" is the y-intercept. The slope of the line is whatever number is multiplied on the "x" variable, so just solve the equation for "x" to figure out the slope! For tips on finding the slope when you're given two points on a graph, read on!

      Did this summary help you?

      In other languages

      Spanish

      German

      Chinese

      Russian

      French

      Indonesian

      Dutch

      Arabic

      Turkish

      • Print
      • Send fan mail to authors

      Thanks to all authors for creating a page that has been read 603,446 times.

      Reader Success Stories

      • How to Find the Slope of an Equation: 3 Easy Methods (67)

        Gabrielle Winful

        Mar 9, 2017

        "It helped me a lot, I just needed to know how to find the slope with a word problem. Other then that, it was..." more

      More reader storiesHide reader stories

      Did this article help you?

      Advertisem*nt

      How to Find the Slope of an Equation: 3 Easy Methods (2024)

      References

      Top Articles
      Latest Posts
      Article information

      Author: Msgr. Benton Quitzon

      Last Updated:

      Views: 5551

      Rating: 4.2 / 5 (43 voted)

      Reviews: 82% of readers found this page helpful

      Author information

      Name: Msgr. Benton Quitzon

      Birthday: 2001-08-13

      Address: 96487 Kris Cliff, Teresiafurt, WI 95201

      Phone: +9418513585781

      Job: Senior Designer

      Hobby: Calligraphy, Rowing, Vacation, Geocaching, Web surfing, Electronics, Electronics

      Introduction: My name is Msgr. Benton Quitzon, I am a comfortable, charming, thankful, happy, adventurous, handsome, precious person who loves writing and wants to share my knowledge and understanding with you.