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The slope of a line measures its slope. You can also say that it is a rise on the run or the rise of the line in relation to its transverse movement. Finding the coefficients of a line or using it to find points on the line are important skills in economics, geological sciences, accounting / finance, and many other fields.

Steps

• Get familiar with basic shapes:

Method 1 of 4: Find coefficients graphically

1. Select two points on the line. Represent and record their coordinates on the graph.
   • Remember, the horizontal scale comes first and the horizontal horizontal.
   • For example, you can choose points (-3, -2) and (5, 4).
2. Determines vertical shifts between two points. To do this, you have to compare the two-point square difference. Start with the first point, which is far to the left of the graph, and move until it meets the intersection of the second point.
   • Vertical shifts can be positive or negative, meaning you can shift up or down. If our line moves up and to the right, the horizontal change will be positive. If the line moves down and right, the vertical change is negative.
   • For example, if the intersection of the first point is (-2) and the second point is (-4), you would add 6 points or your vertical shift is 6.
3. Determines horizontal change between two points. To do this, you have to compare the difference between the two points. Start with the first point, the farthest point on the left of the graph, and move forward until you get the coordinate of the second point.
   • Horizontal changes are always positive, meaning you can only go from left to right and never vice versa.
   • For example, if the coordinate of the first point is (-3) and the second point is (5), you would have to add 8, which means your horizontal change is 8.
4. Calculate the ratio of horizontal change on vertical change to determine the coefficient of the angle. The slope is usually a fraction, but it is also an integer.
   • For example, if the vertical change is 6 and the horizontal change is 8 then your slope is. In short, we can:.
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Method 2 of 4: Find the coefficient of the angle by two given points

1. Set up the recipe. Where, m = coefficient of angle, = coordinates of the first point, = coordinates of the second point.
   • Remember that the slope is equal to the vertical change for the horizontal change or. You are using a formula to calculate the vertical (vertical) change on the horizontal (horizontal) change.
2. Substitute the coordinates into the formula. Make sure that the coordinates of the first point () and second point () are in place in the formula. Otherwise, the obtained angle coefficient will be inaccurate.
   • For example, with two points (-3, -2) and (5, 4), your formula would be:.
3. Perform calculations and reduce them if possible. You will get the slope in the form of a fraction or an integer.
   • For example, if your slope is, you should put it in the denominator (Remember that when subtracting negative numbers, you add) and in the numerator. You can shorten to and thus:.
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Method 3 of 4: Find the offset of the origin knowing the coefficient of the angle and a point

1. Set up the recipe. Where, y = the ordinate of any point on the line, m = coefficient of angle, x = the coordinate of any point on the line, and b = the ordinate.
   • is the equation of a line.
   • The degree of origin is the point at which the line intersects the vertical axis.
2. Substitute the values ​​of the coefficients of angles and coordinates of a point on the line. Remember, the slope is equal to the vertical change across the horizontal change. If you need to find the coefficient of angle, refer to the instructions above.
   • For example, if the slope is and (5,4) is a point on the line, the resulting formula is:.
3. Complete and solve the equation, find b. First, multiply the coefficient of the angle and the horizontal. Subtracting the two sides to this product, we obtain b.
   • In the example problem, the equation becomes:. Subtract two sides for, we get. So, toss the degree of origin.
4. Check calculation. On the coordinate graph, represent the known point and, based on the coefficient of angle, draw a line through that point. To find the intersection angle, find the point at which the line crosses the vertical axis.
   • For example, if the slope is and a given point is (5,4), take a point at the coordinate (5,4) and draw other points along the line by counting left 3 and down 4. When drawing a The line going through the points, the resulting line should cut the vertical axis at the point above the origin (0,0).
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Method 4 of 4: Find the original horizontal when knowing the coefficients of angle and the degree of origin

1. Set up the recipe. In which: y = the coordinate of any point on the line, m = coefficient of angle, x = the coordinate of any point on the line and b = the ordinate.
   • is the equation of the line.
   • The origin is the point at which the line crosses the horizontal axis.
2. Generate angle coefficients and toss degrees into the formula. Remember, the slope is equal to the vertical change across the horizontal change. If you need assistance finding the coefficients you can refer to the instructions above.
   • For example, if the slope is and the ordinate is, the resulting formula would be:.
3. Let y be 0. You are looking for the horizontal axis, the point at which the line intersects the horizontal axis. At this point, the ordinate will be 0. So, if y is 0 and solves the obtained equation to find the corresponding coordinate, we get the point (x, 0) - which is the original coordinate.
   • In the example problem, the equation becomes:.
4. Complete and solve the equation, find x. First, subtract the sides from the side to let the offset. Next, divide both sides by the coefficient of the angle.
   • In the example problem, the equation becomes:. Divide both sides by, obtained:. In short, we have:. So the point at which the line passes through the horizontal axis is. So the original is.
5. Check calculation. On the coordinate graph, represent your vertical offset, then, based on the coefficients, draw a line. To find the horizontal axis, find the point at which the line intersects the horizontal axis.
   • For example, if the slope is and the offset is, represent the point and draw other points along the line by counting left 3 and down 4 then right 3 and up 4. When drawing a line through the lines. The obtained point and line should cut the horizontal axis just a little to the left from the origin (0,0).

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