Calculating Slope

Student Summary

One way to calculate the slope of a line is by drawing a slope triangle. For example, using this slope triangle, the slope of the line is -24\text-\frac24, or -12\text-\frac12. The slope is negative because the line is decreasing from left to right.

graph of  a line. point A at 1 comma 5 and point B at 5 comma 3 on the line. right triangle below line showing down 2, right 4 between point A and B.

Another way to calculate the slope of this line uses just the points A:(1,5)A:(1,5) and B:(5,3)B:(5,3). The slope is the vertical change divided by the horizontal change, or the change in the yy-values divided by the change in the xx-values. Between points AA and BB, the yy-value change is 35=-23-5=\text-2 and the xx-value change is 51=45-1=4. This means the slope is -24\text-\frac24, or -12\text-\frac12, which is the same value as the slope calculated using a slope triangle.

Notice that in each of the calculations, the value from point AA was subtracted from the value from point BB. If it had been done the other way around, then the yy-value change would have been 53=25-3=2 and the xx-value change would have been 15=-41-5=\text-4, which still gives a slope of -12\text-\frac12

Visual / Anchor Chart

Standards

Building On
7.NS.A

No additional information available.

Addressing
8.EE.B

No additional information available.

Building Toward
8.EE.6

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.