Example

Graphing x+2y=6-x + 2y = 6 Using Intercepts

To construct the graph of the linear equation x+2y=6-x + 2y = 6 using the intercept method, follow these systematic steps:

Step 1 — Identify the intercepts. For the x-intercept, let y=0y = 0 to get x+2(0)=6-x + 2(0) = 6, which results in x=6x = -6, giving the point (6,0)(-6, 0). For the y-intercept, let x=0x = 0 to get (0)+2y=6-(0) + 2y = 6, which gives 2y=62y = 6 or y=3y = 3, yielding the point (0,3)(0, 3). Step 2 — Determine a third solution. Choose an x-value such as x=2x = 2. Substituting this into the equation gives 2+2y=6-2 + 2y = 6, so 2y=82y = 8 and y=4y = 4. This produces a check point at (2,4)(2, 4). Step 3 — Plot and verify. Map the points (6,0)(-6, 0), (0,3)(0, 3), and (2,4)(2, 4) on the coordinate plane and confirm they form a single straight line. Step 4 — Draw the line. Complete the graph by drawing a continuous line through the plotted points.

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Updated 2026-04-23

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