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Finding the Equation of a Graphed Line Passing Through (0,−5)(0, -5) and (3,−1)(3, -1)

To extract the equation of a line directly from its graphical representation, calculate its slope and visually locate its yy-intercept, then synthesize this information using the slope-intercept form, y=mx+by=mx+b.

Consider a line on a coordinate plane that carries a yy-intercept of (0,−5)(0, -5) and crosses exactly through another point at (3,−1)(3, -1).

Step 1 — Find the slope. Determine the vertical and horizontal positional changes between the two integer coordinates. Progressing from (0,−5)(0, -5) to (3,−1)(3, -1), the upward vertical rise is 44 units and the rightward horizontal run is 33 units.

m=riserun=43m = \frac{\text{rise}}{\text{run}} = \frac{4}{3}

Step 2 — Identify the yy-intercept. Based strictly on the visual plotted line, the intersection with the yy-axis is (0,−5)(0, -5), meaning b=−5b = -5.

Step 3 — Substitute into y=mx+by = mx + b.

y=43x+(−5)y = \frac{4}{3}x + (-5)

y=43x−5y = \frac{4}{3}x - 5

The full mathematical equation for the provided graph is y=43x−5y = \frac{4}{3}x - 5.

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Updated 2026-05-03

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References

Tags

OpenStax

Intermediate Algebra @ OpenStax

Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax

Algebra

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