This article was coauthored by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.
There are 8 references cited in this article, which can be found at the bottom of the page.
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The slope of a line measures how steep the line is. ^{[1] X Research source } You could also say it is the rise over the run; that is, how much the line rises vertically compared with how much it runs horizontally. Being able to find the slope of a line, or using the slope to find points on the line, is an important skill used in economics, ^{[2] X Research source } geoscience, ^{[3] X Research source } accounting/finance and other fields.
Steps
Method 1
Method 1 of 4:Using a Graph to Find the Slope

1Pick two points on the line. Draw dots on the graph to represent these points, and note their coordinates.
 Remember when graphing points to list the xcoordinate first, then the ycoordinate.
 For example, you might choose the points (3, 2) and (5, 4).

2Determine the rise between the two points. To do this, you must compare the difference in y of the two points. Begin with the first point, the point that is the farthest left on the graph, and count up until you reach the ycoordinate of the second point.
 The rise can be positive or negative; that is, you can count up or down to find it.^{[4] X Research source } If the line is moving up and to the right, the rise is positive. If the line is moving down and to the right, the rise is negative. ^{[5] X Research source }
 For example, if the ycoordinate of the first point is (2), and the ycoordinate of the second point is (4), you will count up 6 points, so your rise is 6.
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3Determine the run between the two points. To do this, you must compare the difference in x of the two points. Begin with the first point, the point that is farthest left on the graph, and count over until you reach the xcoordinate of the second point.
 To run is always positive; that is, you can only count from left to right, never right to left. ^{[6] X Research source }
 For example, if the xcoordinate of the first point is (3), and the xcoordinate of the second point is (5), you will count over 8, so your run is 8.

4Make a ratio using the rise over the run to determine the slope. The slope is usually in fraction form, but it can also be a whole number.
 For example, if the rise is 6 and the run is 8, then your slope is , which can be simplified to .
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Method 2
Method 2 of 4:Using Two Given Points to Find the Slope

1Set up the formula . In the formula, m = the slope, = the coordinates of the first point, = the coordinates of the second point.
 Remember that the slope is equal to . You are using this formula to find the change in y (rise) over the change in x (run). ^{[7] X Research source }

2Plug the x and ycoordinates into the formula. Make sure you place the coordinates of the first point () and the second point () in the correct positions in the formula, or else you will not calculate the correct slope.
 For example, given the points (3, 2) and (5, 4), your formula will look like this: .

3Complete the calculation and simplify, if possible. This will give you the slope as a fraction or whole number.
 For example, if your slope is you should calculate in the numerator (Remember when subtracting a negative number, you add.) and in the denominator. You can simplify to , so .
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Method 3
Method 3 of 4:Finding the yintercept, Given the Slope and One Point

1Set up the formula . In the formula, y = the ycoordinate of any point on the line, m = slope, x = the xcoordinate of any point on the line, and b = the yintercept.
 is the equation of a line. ^{[8] X Research source }
 The yintercept is the point at which the line crosses the yaxis.
EXPERT TIPMath Instructor, City College of San FranciscoGrace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.Grace Imson, MA
Math Instructor, City College of San FranciscoOur Expert Agrees: If you have the slope and one point, plug them into the equation of the line. In y = mx + b, m is the slope, and the point coordinate will contain both x and y. Then, solve for b to find the yintercept.

2Plug in the slope and the coordinates of one point in the line. Remember, the slope is equal to the rise over the run. If you need help finding the slope, see the instructions above.
 For example, if the slope is , and on point on the line is (5,4), then the formula will look like this: .

3Complete the equation, solving for b. First multiply the slope and the xcoordinate. Subtract this number from both sides to solve for b.
 In the example problem the equation becomes . Subtracting from both sides, you end up with . So the yintercept is .

4Check your work. On a coordinate graph, plot your known point, then draw a line using the slope. To find the yintercept, look for the point where the line crosses the yaxis.
 For example, if the slope is , and one point is (5,4), draw a point at (5,4), then draw other points along the line by counting to the left 4 and down 3. When you draw a line through the points, you should see the line cross the yaxis just above the (0,0) coordinate.
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Method 4
Method 4 of 4:Finding the xintercept, Given the Slope and Yintercept

1Set up the formula . In the formula, y = the ycoordinate of any point on the line, m = slope, x = the xcoordinate of any point on the line, and b = the yintercept.
 is the equation of a line. ^{[9] X Research source }
 The xintercept is the point at which the line crosses the xaxis.

2Plug the slope and yintercept into the formula. Remember, the slope is equal to the rise over the run. If you need help finding the slope, see the instructions above.
 For example, if the slope is , and the yintercept is , the formula will look like this: .

3Set y to 0. ^{[10] X Research source } You are looking for the xintercept, the point at which the line crosses the xaxis. At this point, the ycoordinate will equal zero. So if we set y to 0, and solve for the corresponding xcoordinate, we will find the point (x, 0), which will be the xintercept.
 In the example problem, the equation becomes .

4Complete the equation, solving for x. First subtract the yintercept from both sides. Then divide both sides by the slope.
 In the example problem the equation becomes . Dividing both sides by , you end up with . This simplifies to . So the point at which the line crosses the xaxis is . So the xintercept is .

5Check your work. On a coordinate graph, plot your yintercept, then draw a line using the slope. To find the xintercept, look for the point where the line crosses the xaxis.
 For example, if the slope is , and the yintercept is , draw a point at , then draw other points along the line by counting to the left 4 and down 3, and to the right 3 and up 4. When you draw a line through the points, you should see the line cross the xaxis just left of the (0,0) coordinate.

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Community Q&A

QuestionHow do I write an equation for the line with a slope of 6 and yintercept of 3?DonaganTop AnswererUse the formula y = mx + b, where m is the slope and b is the yintercept.

QuestionHow do I write the equation of a line, given the slope and yintercept?DonaganTop AnswererAssuming you're talking about a linear (straightline) equation, you would use the standard slope/yintercept form, y = mx + b. Use the given slope for m, the coefficient of x. Use the given yintercept for b, the constant in the equation. For example, if the slope is 3 and the yintercept is 5, the equation would be y = mx + b = 3x + (5) = 3x  5.

QuestionWhat is intercept and how do I calculate this using a graph?Community AnswerThere are two types of intercept, xintercept and yintercept. When we say xintercept, this means the line passes through the xaxis with coordinates (x,0). When we say yintercept, the graph passes through the yaxis with coordinates (0,y). To find x or y intercepts, just observe where the line on the graph cuts the x or y axis respectively.

QuestionWhat is simultaneous linear graph?DonaganTop AnswererThat is a graph showing more than one function, equation, or line.

QuestionIf point (2,4) has a slope of 4, what is the equation?DonaganTop AnswererThe standard equation is y = mx + b, where m is the slope, and b is the yintercept. The slope is given as 4. Thus, y = 4x + b. The point (2,4) fits into the equation, so we can insert those x and y values into the equation. Thus, 4 = 4(2) + b = 8 + b. Adding 8 to both sides of the equation results in 4 = b. Thus, the equation we're looking for is y = mx + b = 4x + 4.

QuestionWhat is the slope of a line that has a y intercept of 5 and an x intercept of 5?OrangejewsCommunity AnswerWith two points, (0,5) and (5,0), you can compute slope directly by dy/dx. The slope = dy/dx = (50)/(0(5))= 1.

QuestionIf the x interecept is 3/4 and the line passes through the points 2,1/3 what is the slope?Community AnswerYou are given two points: (3/4, 0) and (2, 1/3). Slope is defined as rise over run or delta y over delta x, so plug the known coordinates into that formula. Slope = (0  1/3) / (3/4  (2)) = (1/3) / (5/4) = 4/15.

QuestionHow do I find the yintercept of the equation 2(x1)^2 + 5?DonaganTop AnswererThe yintercept occurs when x=0. So substitute 0 for x in the equation, and solve for y. y = 2(x1)² + 5. Substituting 0 for x: y = 2(01)² + 5 = 2(1)² + 5 = 2(1) + 5 = 2 + 5 = 7. So y is 7 when x is 0, and the yintercept is 7.

QuestionHow can I find a correct scale for a graph?DonaganTop AnswererTake the maximum quantity to be represented on either axis, and divide it by the number of units available on that axis. The quotient will be the quantity to be represented by each unit. This can be done separately for each axis, although typically a single scale is used for both axes.

QuestionHow do I find x and y of a line?Community AnswerX is the sideways line, y is the upwards/downward line. Namely, x is vertical, y is horizontal.
References
 ↑ http://www.mathopenref.com/coordslope.html
 ↑ http://www.columbia.edu/itc/sipa/math/slope_linear.html
 ↑ http://serc.carleton.edu/mathyouneed/slope/slopes.html
 ↑ http://www.coolmath.com/algebra/08lines/05findingslopelinefromgraph01
 ↑ http://www.mathopenref.com/coordslope.html
 ↑ http://www.coolmath.com/algebra/08lines/05findingslopelinefromgraph01
 ↑ http://www.coolmath.com/algebra/08lines/06findingslopelinegiventwopoints01
 ↑ http://www.mathopenref.com/coordequation.html
 ↑ http://www.mathopenref.com/coordequation.html
 ↑ https://www.youtube.com/watch?v=wPs0tjl8Vpg
 The workbook used to write this article was "y = ax + b.xlsx"
About This Article
To find the slope of a line from a graph, first choose 2 points along the line and write down the X and Y coordinates for each. Next, find the rise by taking the difference between the 2 Y coordinates. If the line slopes up as it moves to the right, the rise will be positive. If it slopes down, the rise will be negative. Once you’ve found the rise, calculate the run by finding the difference between the 2 X coordinates, going from left to right. Finally, find the slope by dividing the rise by the run. Keep reading for more tips, including how to find the Yintercept using the slope and 1 point!