Question
Solve the inequality graphically in a two-dimensional plane: 3x + 4y $\leq$ 12
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Answer
The given inequality is $3x + 4y \leqslant 12$
Draw the graph of line 3x + 4y = 12
Table of values satisfying the equation
3x + 4y = 12
Draw the graph of line 3x + 4y = 12
Table of values satisfying the equation
3x + 4y = 12
| X | 0 | 4 |
| Y | 3 | 0 |
Putting (0, 0) in the given in equation, we have $3 \times 0 + 4 \times 0 \leqslant 12 \Rightarrow 0 \leqslant 12$ which is true.
$\therefore $ Half plane of $3x + 4y \leqslant 12$ is towards origin.
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