Graph the solution sets of the following inequations: $x+2 y>1$

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Graph the solution sets of the following inequations: $x+2 y>1$

Given $x+2 y>1$
$\begin{array}{l} \Rightarrow 2 y>1-x \\ \Rightarrow y>\frac{1}{2}-\frac{x}{2} \end{array}$
Consider the equation $y=\frac{1}{2}-\frac{x}{2}$
Finding points on the coordinate axes:
If $x=0$ , the $y$ value is $\frac{1}{2}$ i.e., $y=4$
$\Rightarrow$ the point on the $Y$ axis is $A\left(0, \frac{1}{2}\right)$
If $y=0, x=1$
The point on the $X$ axis is $B(1,0)$
Plotting the points on the graph: fig. $3 a$

Now consider the inequality $y>\frac{1}{2}-\frac{x}{2}$
Here we need the $\mathrm{y}$ value greater than $\frac{1}{2}-\frac{x}{2}$
$\Rightarrow$ the required region is above point $A$ .
Also, the line $A B$ is represented in dotted line. This is s done because $y \neq \frac{1}{2}-\frac{x}{2}$
Therefore the graph of the inequation $y>\frac{1}{2}-\frac{x}{2}$ is fig. $3 \mathrm{~b}$