Finding the Equation of a Graphed Line Passing Through and
To extract the equation of a line directly from its graphical representation, calculate its slope and visually locate its -intercept, then synthesize this information using the slope-intercept form, .
Consider a line on a coordinate plane that carries a -intercept of and crosses exactly through another point at .
Step 1 — Find the slope. Determine the vertical and horizontal positional changes between the two integer coordinates. Progressing from to , the upward vertical rise is units and the rightward horizontal run is units.
Step 2 — Identify the -intercept. Based strictly on the visual plotted line, the intersection with the -axis is , meaning .
Step 3 — Substitute into .
The full mathematical equation for the provided graph is .
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Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
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Finding the Equation of a Graphed Line Passing Through and
Finding the Equation of a Graphed Line Passing Through and
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