1Cademy - Finding the Slope $$-\frac{4}{3}$$ from a Graph

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Finding the Slope of a Line from its Graph

Example

Finding the Slope $-\frac{4}{3}$ from a Graph

A line is graphed on the $xy$ -coordinate plane passing through the points $(0, -2)$ and $(3, -6)$ . To find its slope, apply the four-step rise-over-run procedure.

Step 1 — Locate two points with integer coordinates. The points $(0, -2)$ and $(3, -6)$ both have integer coordinates. The leftmost point is $(0, -2)$ .

Step 2 — Sketch a right triangle. Starting at the left point $(0, -2)$ , draw a vertical leg downward to $(0, -6)$ and then a horizontal leg to the right to reach $(3, -6)$ .

Step 3 — Count the rise and the run. The vertical leg goes from $-2$ down to $-6$ , so the rise is $-4$ (negative because the line moves downward). The horizontal leg goes from $0$ to $3$ , so the run is $3$ .

Step 4 — Take the ratio of rise to run:

$m = \frac{\text{rise}}{\text{run}} = \frac{-4}{3} = -\frac{4}{3}$

The slope of the line is $-\frac{4}{3}$ . This provides another example of a negative slope, where the line drops $4$ units for every $3$ units it moves to the right.

Updated 2026-05-03

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OpenStax Intermediate Algebra

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