To find the slope of a line given two points (x1,y1)(x_1,y_1)(x1,y1) and (x2,y2)(x_2,y_2)(x2,y2), use the slope formula:
m=y2−y1x2−x1m=\frac{y_2-y_1}{x_2-x_1}m=x2−x1y2−y1
Here, mmm represents the slope, which is the ratio of the vertical change (rise) to the horizontal change (run) between the two points. The steps are:
- Identify the coordinates of the two points: (x1,y1)(x_1,y_1)(x1,y1) and (x2,y2)(x_2,y_2)(x2,y2).
- Calculate the difference in the y-values: y2−y1y_2-y_1y2−y1.
- Calculate the difference in the x-values: x2−x1x_2-x_1x2−x1.
- Divide the difference in y by the difference in x to get the slope mmm.
For example, to find the slope between points (1,−2)(1,-2)(1,−2) and (3,−6)(3,-6)(3,−6):
m=−6−(−2)3−1=−6+22=−42=−2m=\frac{-6-(-2)}{3-1}=\frac{-6+2}{2}=\frac{-4}{2}=-2m=3−1−6−(−2)=2−6+2=2−4=−2
So, the slope is −2-2−2
. This formula works regardless of which point you label first, as switching the order will cancel out the negative signs. The slope indicates how steep the line is and the direction it moves across the graph.
