1Cademy - Graphing $$3x - 4y = 12$$ Using Intercepts

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Graphing a Line Using the Intercept Method

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Graphing $3x - 4y = 12$ Using Intercepts

To graph the linear equation $3x - 4y = 12$ using the intercept method:

Step 1 — Locate the intercepts. To acquire the x-intercept, configure $y = 0$ : $3x - 4(0) = 12$ , giving $3x = 12$ , so $x = 4$ resulting in $(4, 0)$ . To gain the y-intercept, set $x = 0$ : $3(0) - 4y = 12$ , generating $-4y = 12$ and $y = -3$ yielding $(0, -3)$ . Step 2 — Determine an extra solution. Assume $y = 3$ : replacing this into the equation results in $3x - 4(3) = 12$ , which becomes $3x - 12 = 12$ , so $3x = 24$ meaning $x = 8$ . Complete the ordered pair as $(8, 3)$ . Step 3 — Plot the coordinates. Plot the three points $(4, 0)$ , $(0, -3)$ , and $(8, 3)$ accurately onto a graph, ensuring consistent linear alignment. Step 4 — Draw the line. Securely draw the graph by creating a straight line uniting the three mapped plots.

Updated 2026-04-23

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OpenStax Intermediate Algebra

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