Draw the graph of the equation $\frac{x}{3} + \frac{y}{4} = 1.$ Also, find the area of the triangle formed by the line and the coordinates axes.

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Solution

$\frac{x}{3} + \frac{y}{4} = 1 \Rightarrow 4 x + 3 y = 12 \Rightarrow 4 x = 12 - 3 y x = \frac{12 - 3 y}{4} I f y = 0, t h e n x = \frac{12 - 3 \times 0}{4} = \frac{12 - 0}{4} = \frac{12}{4} = 3 I f y = 4, t h e n x = \frac{12 - 3 \times 4}{4} = \frac{12 - 12}{4} = \frac{0}{4} = 0$

$\begin{matrix} x & 3 & 0 y & 0 & 4 \end{matrix}$

Now plot the points (3, 0) and (0, 4) on join them to get a line which interest x-axis at A (3, 0) and y-axis at B (0, 4)

Area of the $Δ A O B = \frac{1}{2} \times O A \times O B$

$= \frac{1}{2} \times 3 \times 4 s q . u n i t s = 6 s q . u n i t s$

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Draw the graph of the line 4x + 3y = 24.

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(ii) Use this graph to find the area of the triangle formed by the graph line and the coordinate axes.

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