1Cademy - Finding the Slope $$-\frac{2}{3}$$ from a Graph

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Finding the Slope of a Line from its Graph

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Finding the Slope $-\frac{2}{3}$ from a Graph

A line is graphed on the $xy$ -coordinate plane passing through the points $(0, 5)$ , $(3, 3)$ , and $(6, 1)$ . To find its slope, apply the four-step rise-over-run procedure.

Step 1 — Locate two points with integer coordinates. The points $(0, 5)$ and $(3, 3)$ both have integer coordinates. The leftmost point is $(0, 5)$ .

Step 2 — Sketch a right triangle. Starting at the left point $(0, 5)$ , draw a vertical leg downward to $(0, 3)$ and then a horizontal leg to the right to reach $(3, 3)$ .

Step 3 — Count the rise and the run. The vertical leg goes from $5$ down to $3$ , so the rise is $-2$ (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:

$m = \frac{\text{rise}}{\text{run}} = \frac{-2}{3} = -\frac{2}{3}$

The slope of the line is $-\frac{2}{3}$ .

To verify, use a different pair of points on the same line: $(-3, 7)$ and $(6, 1)$ . The rise is $-6$ and the run is $9$ , giving $m = \frac{-6}{9} = -\frac{2}{3}$ . This confirms an important property: no matter which two points on a line are chosen, the calculated slope is always the same.

Updated 2026-05-03

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