Draw the graph of 3x + 2y = 12. Find the x-intercept and y-intercept. Also, check whether (2, 3) lies on this line.

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STEP 1 — FIND X-INTERCEPT: Set y = 0: 3x + 2(0) = 12 → 3x = 12 → x = 4. X-intercept = (4, 0). STEP 2 — FIND Y-INTERCEPT: Set x = 0: 3(0) + 2y = 12 → 2y = 12 → y = 6. Y-intercept = (0, 6). STEP 3 — FIND A THIRD POINT (to verify): Set x = 2: 3(2) + 2y = 12 → 6 + 2y = 12 → 2y = 6 → y = 3. Point (2, 3). STEP 4 — GRAPH: Plot (4, 0), (0, 6), and (2, 3). Draw a straight line through all three. STEP 5 — CHECK (2, 3): LHS = 3(2) + 2(3) = 6 + 6 = 12 = RHS ✓. Yes, (2, 3) lies on the line. In fact, it was our third point! ANSWER: X-intercept = 4, Y-intercept = 6. (2, 3) DOES lie on the line.

Practice — Linear Equations in Two Variables

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