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Determine slope from a graph

Slope is the constant rate of change of a linear relationship, found from a graph by comparing the vertical change (rise) with the horizontal change (run) between two points: m=y2−y1x2−x1m=\frac{y_2-y_1}{x_2-x_1}. Its sign indicates whether the line increases or decreases, its magnitude describes steepness, and a horizontal line has slope zero; the focus is on straight-line graphs rather than nonlinear or calculus-based rates of change.

Detailed Explanation: Determine slope from a graph

Slope tells how much a line changes vertically for each 1-unit change horizontally. Find it by comparing the rise to the run:

m=riserun=y2−y1x2−x1m=\frac{\text{rise}}{\text{run}}=\frac{y_2-y_1}{x_2-x_1}

Example

Suppose a straight line on a graph passes through the points (1,2)(1,2) and (4,8)(4,8).

  1. Choose two points on the line.
    Let (x1,y1)=(1,2)(x_1,y_1)=(1,2) and (x2,y2)=(4,8)(x_2,y_2)=(4,8).

  2. Find the vertical change, or rise.

rise=y2−y1=8−2=6\text{rise}=y_2-y_1=8-2=6

  1. Find the horizontal change, or run.

run=x2−x1=4−1=3\text{run}=x_2-x_1=4-1=3

  1. Divide the rise by the run.

m=63=2m=\frac{6}{3}=2

The slope is 2\boxed{2}. This means that for every 11 unit the line moves to the right, it rises 22 units.

A line that rises from left to right has a positive slope. A line that falls from left to right has a negative slope, and a horizontal line has slope 00.

Learn by doing: Determine slope from a graph

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    Slope of a Line Between Two Points on Graph - Integer

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