How to Measure the Slope of a Line
The slope of a line is a term for how steep a line is. The steps for calculating the slope of a graphed line can be used to solve practical problems. For example, slope can be used to describe the steepness of a hill or staircase.
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Instructions
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Think of slope as a ratio. It compares the distance a line rises vertically to the distance the line runs horizontally. This math concept is commonly described using a fraction, "rise over run."
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Picture slope. Envision walking a straight line. If you walk uphill, the slope is positive because the rise and run are both positive. If you walk downhill, the slope is negative because the rise is decreasing while the run is increasing. If you walk on level ground, slope is zero because the rise is zero.
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Examine a line on graph paper. A graphed line always appears in relation to a vertical line called the Y axis and a horizontal line called the X axis. The X axis and Y axis intersect at a right angle. The point of intersection is called the origin.
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Pick 2 points on the line. Each point has a first and last name. The first name is called its X coordinate. It is the number of units on the X axis from the origin. The last name is called the Y coordinate. It is the number of units on the Y axis from the origin.
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Calculate rise and run. Using simple math, subtract the 2 Y coordinates. The difference represents the rise. Subtract the 2 X coordinates, following the same order of subtraction, to obtain the run. For example, if the first point is (1,2) and the second point is (3,5). The rise is 5 minus 2, which equals 3. The run is 3 minus 1, which equals 2.
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Apply the formula. Using simple math, divide rise by run. If the rise is 3 and the run is 2, then the slope is 3 over 2.
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Interpret the slope. A slope of 3 over 2 is somewhat steep because the line rises at a faster rate than it runs.
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Tips & Warnings
When subtracting coordinates, the order in which the points are used does not matter provided the X coordinates are subtracted in the same order as the Y coordinates
Calculated slopes should match appearance. For example, if a graphed line moves downward as it travels left to right, but the calculated slope is positive, revisit the math. It has been calculated incorrectly.
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Comments
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Calculated slopes should match appearance. For example, if a graphed line moves downward as it travels left to right, but the calculated slope is positive, revisit the math. It has been calculated incorrect.
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aelaena
Dec 04, 2009
THANK YOU helped me in math 5*'s
