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in Geometry and Algebra by (30.8k points)
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Prove that for any point on the line intersecting the axes in the picture, the sum of the x and y coordinates is 3.

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If (x, y) lies' on the line joining the points (0,3) and (3,0) then,

\(\frac{y-3}{x-0}=\frac{0-3}{3-0}\)

\(\Rightarrow \frac{y-3}{x}=\frac{-3}{3}=-1\)

y - 3 = x

\(\Rightarrow\) x + y = 3

∴ the sum of the and y coordinates of the point is 3.

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