In math, the slope describes how steep a straight line is. It is sometimes called the gradient.

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Equations for SlopeThe slope is defined as the "change in y" over the "change in x" of a line. If you pick two points on a line --- (x1,y1) and (x2,y2) --- you can calculate the slope by dividing y2 - y1 over x2 - x1.Here are the formulas used to find the slope of a line:

This line goes through the points (0,0) and (3,3).Slope = (y2 - y1)/(x2 - x1)= (3 - 0)/(3 - 0)= 3/3= 1This line has a slope of 1. Try using different points on the line. You should get the same slope regardless of what points you use.

You can see that the line contains the points (-2,4) and (2, -2).Slope = (y2 - y1)/(x2 - x1)= (-2 - 4))/(2 - (-2))= -6/4= - 3/2Special CasesSome special cases include horizontal and vertical lines.A horizontal line is flat. The change in y is 0, so the slope is 0.A vertical line has a change in x of 0. Since you can"t divide by 0, a vertical line has an undefined slope.Up or Down - Positive or Negative SlopeIf you look at the line from left to right, a line that is moving up will have a positive slope and a line that is moving down will have a negative slope. You can see this on the two example problems above.
Rise over RunAnother way to remember how the slope works is "rise over run". You can draw a right triangle using any two points on the line. The rise is the distance that the line travels up or down. The run is the distance that the line travels from left to right.

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Things to RememberSlope = change in y over the change in xSlope = (y2 - y1)/(x2 - x1)Slope = rise over runYou can pick any two points on a line to calculate the slope.You can double check your answer by trying different points on the line.If the line is going up, from left to right, the slope is positive.If the line is going down, from left to right, the slope is negative.More Geometry SubjectsCirclePolygonsQuadrilateralsTrianglesPythagorean TheoremPerimeterSlopeSurface AreaVolume of a Box or CubeVolume and Surface Area of a SphereVolume and Surface Area of a CylinderVolume and Surface Area of a ConeAngles glossaryFigures and Shapes glossary

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