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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.
Steps
Method 1
Method 1 of 3:Finding the Slope of a Linear Equation

1Use 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:
 There are no exponents on the variables
 There are only two variables, neither of which are fractions (for example, you would not have
 The equation can be simplified to the form , where m and b are constants (numbers like 3, 10, 12, ).^{[1] X Research source }

2Find the number in front of the x, usually written as "m," to determine slope. If your equation is already in the right form, , 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:

 Slope = 2

 Slope = 1

 Slope = ^{[2] X Research source }
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3Reorganize 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 . For example:
 Find the slope of

Set to the form :

Find the slope:
 Slope = M = 4^{[3] X Research source }
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Method 2
Method 2 of 3:Finding the Slope with Two Points

1Use 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 . While finding the slope, keep in mind the following information to help you check if you're on the right track:
 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."^{[4] X Research source }

2Find 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).^{[5] X Research source }
 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.

3Label your points x_{1}, y_{1}, x_{2}, y_{2}, 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:
 x_{1}: 2
 y_{1}: 4
 x_{2}: 6
 y_{2}: 6^{[6] X Research source }

4Plug your points into the "PointSlope Formula" to get your slope. The following formula is used to find slope using any two points on a straight line: . Simply plug in your four points and simplify:
 Original Points: (2,4) and (6,6).

Plug into Point Slope:

Simplify for Final Answer:
 = Slope

5Understand how the PointSlope 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 yvalues (remember, the Yaxis goes up and down), and the “run” of the line is the difference between the xvalues (and the Xaxis goes left and right).

6Recognize other ways you may be tested to find slope. The equation of the slope is . 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 betweenAdvertisement
Method 3
Method 3 of 3:Using Differential Calculus to Find the Slope of a Curve

1Review 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.

2Understand 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).
 For this method, consider the question: "What is the slope of the line at the point (4,2)?"^{[7] X Research source }
 The derivative is often written as or ^{[8] X Research source }

3Take 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, . Following the methods outlined here, take the derivative of this simple function.
 Derivative:

4Plug 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 at the point (4,2)?

Derivative of Equation:

Plug in Point for x:
 Find the Slope:
 The slope of the at (4,2) is 22.

5Check 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.
 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.
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Community Q&A

QuestionWhat is the slope for the equation y=1?DonaganTop AnswererThe 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.

QuestionWhat if the equation is like x+y=0 or xy=0?Community AnswerThat's no problem. When x+y=0, y=x. In this case the slope is 1. On the other hand, when xy=0, y=x. Here the slope is +1.

QuestionWhat's the difference between a slope = 0 and slope = undefined?DonaganTop AnswererA zero slope is a horizontal line (parallel to the xaxis), and an undefined slope is a vertical line (parallel to the yaxis).

QuestionSlope of a line 2x  y +9?DonaganTop AnswererIf the equation is 2x  y + 9 = 0, rewrite it as y = 2x + 9. Once the equation is written in that form, the slope is seen as the coefficient of the independent variable (x in this case). So the slope is 2.

QuestionHow do I find the slope given a single point on a straight line?DonaganTop AnswererIf all you're given are the coordinates of a single point on a line, you cannot find a line's slope. You would need the coordinates of at least one more point.

QuestionHow do I find the slope in a word problem?DonaganTop AnswererYou would have to write an equation that reflects the conditions stated in the word problem. If you can write it in (or change it to) the form y = mx + b, the slope will be the xcoefficient (m).

QuestionSo is the slope of y=2 .2?Community AnswerNo. y = 2 is graphed as a horizontal line, meaning its slope is zero. Put another way, there is no xterm in the equation y = 2, meaning that the xcoefficient is zero. The xcoefficient is also the slope.

QuestionHow do I find the equation of a vertical line containing the point (2,5)?Community AnswerIts equation is x=2.

QuestionHow would I find the slope of the line y = 4?DonaganTop AnswererAny line whose equation is y = k (where k is any constant) will be horizontal (that is, parallel to the xaxis) and therefore will have a slope of zero. Another way of explaining it is to view y = 4 in the slopeintercept form: y = mx + b, where m (the slope) is zero (and b is 4).

QuestionHow do I find the slope intercept equation using only one set of points?DonaganTop AnswererIf you mean that the only information given is one point on the line, that's not enough information to define a line. You must have at least two points to define a straight line, or you must know one point and the slope.
Video
Tips
References
 ↑ http://www.numbertheory.org/book/cha1.pdf
 ↑ https://www.ixl.com/math/grade8/findtheslopeofagraph
 ↑ http://www.mathwarehouse.com/algebra/linear_equation/slopeofaline.php
 ↑ http://www.mathwarehouse.com/algebra/linear_equation/slopeofaline.php
 ↑ http://www.virtualnerd.com/algebra1/linearequationanalysis/sloperateofchange/slopeexamples/slopefromgraph
 ↑ http://www.mathwarehouse.com/algebra/linear_equation/slopeofaline.php
 ↑ https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/implicitdiffdirectory/ImplicitDiff.html
 ↑ http://archives.math.utk.edu/visual.calculus/3/implicit.7/index.html
About This Article
To find the slope of a linear equation, start by rearranging the given equation into slopeintercept form, which is y = mx + b. In slopeintercept form, "m" is the slope and "b" is the yintercept. 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!