You can also use this method if you are given two points on the line, without having the line graphed in front of you. Coordinates are listed as (x,y){\displaystyle (x,y)}, with x{\displaystyle x} being the location along the x, or horizontal axis, and y{\displaystyle y} being the location along the y, or vertical axis. For example, you might choose points with coordinates (3,2){\displaystyle (3,2)} and (7,8){\displaystyle (7,8)}.
The first point’s coordinates will be (x1,y1){\displaystyle (x_{1},y_{1})}, and the second point’s coordinates will be (x2,y2){\displaystyle (x_{2},y_{2})}
For example, if the coordinates of your first point are (3,2){\displaystyle (3,2)}, and the coordinates of your second point are (7,8){\displaystyle (7,8)}, your formula will look like this:riserun=8−2x2−x1{\displaystyle {\frac {rise}{run}}={\frac {8-2}{x_{2}-x_{1}}}}
For example, if the coordinates of your first point are (3,2){\displaystyle (3,2)}, and the coordinates of your second point are (7,8){\displaystyle (7,8)}, your formula will look like this:riserun=8−27−3{\displaystyle {\frac {rise}{run}}={\frac {8-2}{7-3}}}
For example, if your y-coordinates are 8{\displaystyle 8} and 2{\displaystyle 2}, you would calculate 8−2=6{\displaystyle 8-2=6}.
For example, if your x-coordinates are 7{\displaystyle 7} and 3{\displaystyle 3}, you would calculate 7−3=4{\displaystyle 7-3=4}.
For complete instructions on how to reduce a fraction, read Reduce Fractions. For example, 64{\displaystyle {\frac {6}{4}}} can be reduced to 32{\displaystyle {\frac {3}{2}}}, so the slope of a line through points (3,2){\displaystyle (3,2)} and (7,8){\displaystyle (7,8)} is 32{\displaystyle {\frac {3}{2}}}.
Remember, if the numerator and denominator are both negative, then the negative signs cancel out, and the fraction (and slope) is positive. If either the numerator or the denominator is negative, then the fraction (and slope) is negative.
If you do not reach your second point, then your calculation is incorrect.
