1Cademy - Graphing $$5x - 2y = 10$$ Using Intercepts

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Graphing a Line Using the Intercept Method

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Graphing $5x - 2y = 10$ Using Intercepts

To construct the graph of $5x - 2y = 10$ using the intercept method:

Step 1 — Determine the intercepts. Evaluate the x-intercept by setting $y = 0$ : $5x - 2(0) = 10$ , so $5x = 10$ yielding $x = 2$ and the point $(2, 0)$ . Evaluate the y-intercept by placing $x = 0$ : $5(0) - 2y = 10$ , leading to $-2y = 10$ and thus $y = -5$ producing $(0, -5)$ . Step 2 — Find a third verifying point. Try substituting $x = 4$ : this provides $5(4) - 2y = 10$ , which simplifies to $20 - 2y = 10$ , thus $-2y = -10$ and $y = 5$ . This forms the point $(4, 5)$ . Step 3 — Plot and confirm collinearity. Plot the ordered pairs $(2, 0)$ , $(0, -5)$ , and $(4, 5)$ to verify they create a straight line. Step 4 — Draw the line. Hand-draw a continuous straight line connecting the tested coordinate points.

Updated 2026-04-23

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OpenStax Intermediate Algebra

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