Question

Graph the linear inequality:

$x-y<-3$

Short answer

The solution is

Step-by-step solution

Given data

The inequality is

$x-y<-3$

Concept used

First, we draw the boundary line $x-y=-3$.

Here the inequality is $<$.

So, we draw the dashed line as below,

Point test

We test the point $\left(0,0\right)$.

$x-y<-3$

$0-0<-3$

$0<-3$

Which is not possible.

So, $\left(0,0\right)$is not a solution of the inequality $x-y<-3$.

Conclusion

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

The graph will be

All points in the shaded region, but not those on the boundary line, represent the solutions to $x-y<-3$.