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Finding the Equation of a Graphed Line Passing Through (0,1)(0, 1) and (5,4)(5, 4)

When determining the equation of a line from its visual graph, identify the slope and yy-intercept from the coordinate plane, then enter these values into the slope-intercept form, y=mx+by=mx+b.

Consider a graphed line that crosses the yy-axis at (0,1)(0, 1) and passes through the integer coordinate (5,4)(5, 4).

Step 1 — Find the slope. Select two precise points on the graph, such as (0,1)(0, 1) and (5,4)(5, 4). Starting at (0,1)(0, 1), the line has a vertical rise of 33 units upward and a horizontal run of 55 units to the right.

m=riserun=35m = \frac{\text{rise}}{\text{run}} = \frac{3}{5}

Step 2 — Locate the yy-intercept. Observe where the line crosses the yy-axis. Since it crosses at (0,1)(0, 1), the intercept value is b=1b = 1.

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

y=35x+1y = \frac{3}{5}x + 1

The equation defining the graph is y=35x+1y = \frac{3}{5}x + 1.

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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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