if two points determine a line, why do we need a third point in graphing a linear equation using table of values?

To draw the graph of a linear equation , two points are more than enough to draw a line.

But sometimes we may commit a mistake and then if we draw the line, everything appears good. As two points shall always define a line irrespective of the points are correct or not.

So in order to make sure that the points we obtained are correct , we take a third point to ensure that the two points calculated earlier are correct and all points lie on the same line. If they don't we have committed some mistake.

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step-by-step explanation: