Slope Formula to Find Rise over Run

How to Find Rise Over Run

The rise (change in Y) over run (change in X) can be used to find the slope of each line segment on a graph. Adam Gault / Getty Images

The slope formula is sometimes called "rise over run." The simple way to think of the formula is: M=rise/run. M stands for slope. Your goal is to find the change in the height of the line over the horizontal distance of the line.

  • First, look at a graph of a line and find two points, 1 and 2. You can use any two points on a line. The slope will be the same between any two points on a straight line.
  • Note the X and Y value for each of the points.
  • Now we'll designate the X and Y value for points 1 and 2. We'll use subscripts to identify them in the slope formula.

The formula for the slope of the straight line going through the points (X1, Y1) and (X2, Y2) is given by

M = (Y2 - Y1) / (X2 - X1)

The answer, M is the slope of the line. It can be a positive or negative value.

The subscripts are only used to identify the two points. They are not values or exponents. If you find this confusing, you could give the points names instead. How about Bert and Ernie?

  • Point 1 is now Bert and Point 2 is now Ernie
  • Look at the graph and note their X and Y values:(XBert, YBert) and (XErnie, YErnie)
  • The slope formula is now: M = (YErnie - YBert) / (XErnie - XBert)

Slope Formula Tips and Tricks

The slope formula can give a positive or a negative number as a result. In the case of vertical and horizontal lines, it can also give no answer or the number zero.

  • If the slope is a positive value, the line is rising. The technical term is increasing.
  • If the slope is a negative value, the line is descending. The technical term is decreasing.
  • You can check your math by eyeballing the graph. If you got a negative slope but the line is clearly rising, you made an error. If the line is clearly going down and you got a positive slope, you made an error. It could be you mixed up X and Y and points 1 and 2.
  • Vertical lines have no slope. In the equation, you are dividing by zero, which does not produce a number. If a quiz asks the slope of a vertical line, don't say zero. Say it has no slope.
  • Horizontal lines have a zero slope. Zero is a number. In the equation, you are dividing zero by a number and the result is zero. If a quiz asks the slope of a horizontal line, say zero.
  • Parallel lines have equal slopes. If you find the slope of one line, you don't have to run the formula for the other line. They will be the same. This can save you some time and effort.
  • Perpendicular lines have negative reciprocal slopes. If two lines cross at a right angle, you can find the slope of one and then change the value for the other to negative or positive.