Graph the solution sets of the following inequations: $x+y \geq 4$

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Graph the solution sets of the following inequations: $x+y \geq 4$

Given $x+y \geq 4$
$\Rightarrow y \geq 4-x$
Consider the equation $y=4-x$ .
Finding points on the coordinate axes:
If $x=0$ , the $y$ value is 4 i.e, $y=4$
$\Rightarrow$ the point on the $Y$ axis is $A(0,4)$
If $y=0,0=4-x$
$\Rightarrow x=4$
The point on the $X$ axis is $B(4,0)$
Plotting the points on the graph: fig. 1a

Now consider the inequality $y \geq 4-x$
Here we need the y value greater than or equal to $4-\mathrm{x}$
$\Rightarrow$ the required region is above point $A$ .
Therefore the graph of the inequation $x+y \geq 4$ is fig. $1 b$