Question

Graph the linear inequality:

$y>-2x+1$

Short answer

The solution is

Step-by-step solution

Given data

The inequality is

$y>-2x+1$

Concept used

First, we draw the boundary line $y=-2x+1$.

It is in slope-intercept form $y=mx+b$where$m=-2$and $b=1$

Here the inequality is $>$.

So, we draw a dashed line as bellow,

Point test

We can see that the point $\left(0,0\right)$is not on boundary line.

To check $\left(0,0\right)$is a solution of the inequality or not:

$y>-2x+1$

role="math" localid="1644463411771" $0>-2·0+1$

role="math" localid="1644463421871" $0>0+1$

role="math" localid="1644463430159" $0>1$

Which is not possible.

So, $\left(0,0\right)$is not a solution of the inequality $y>-2x+1$.

Conclusion

Thus, we shade in the side of the boundary line that does not include the point $\left(0,0\right)$.

The graph will be

All points in the shaded region represent the solutions to$y>-2x+1$.