Question

Graph the linear inequality:

$y\ge \frac{3}{2}x$

Short answer

The Solution is

Step-by-step solution

Given data

The inequality is

$y\ge \frac{3}{2}x$

Concept used

First, we draw the boundary line $y=\frac{3}{2}x$.

It is in slope–intercept form role="math" localid="1644460072706" $y=mx+b$.

Where$m=\frac{3}{2}$and$b=0$

Here the inequality is $\ge$.

So, we draw a solid line as below,

Point test

We can see that the point $\left(1,0\right)$is not on the boundary line.

To check $\left(1,0\right)$is a solution of the inequality or not:

$y\ge \frac{3}{2}x$

$0\ge \frac{3}{2}·1$

$0\ge \frac{3}{2}$

Which is not possible.

So,$\left(1,0\right)$is not a solution of the inequality$y\ge \frac{3}{2}x$.

Conclusion

Thus, we shade in the side of the boundary line that does not include the point $\left(1,0\right)$.

The graph will be

All points in the shaded region and on the boundary line represent the solutions to$y\ge \frac{3}{2}x$.