Answer
See below:
Work Step by Step
consider the provided inequalities,
\[y>\frac{3}{2}x-2\]and\[y<4\]
Replace each inequality symbol with an equal sign,
\[y=\frac{3}{2}x-2\]and\[y=4\]
Now, draw the graph of the equation\[y=\frac{3}{2}x-2\]:
Put \[y=0\] for x-intercept and \[x=0\] for y-intercept in the equation \[y=\frac{3}{2}x-2\].
So, the x-intercept is \[\frac{4}{3}\] and y-intercept is \[-2\].
Therefore, the line is passing through \[\left( \frac{4}{3},0 \right)\]and \[\left( 0,-2 \right)\].
Now, consider a test point \[\left( 0,0 \right)\], which lies in the half-plane above the line.
Substitute \[x=0\] and \[y=0\]in \[y>\frac{3}{2}x-2\].
\[\begin{align}
& 0>\frac{3}{2}\cdot 0-2 \\
& 0>-2
\end{align}\]
Since \[\left( 0,0 \right)\]satisfies the above inequality \[y>\frac{3}{2}x-2\].
So, the test point \[\left( 0,0 \right)\] is part of the solution set.
All the points on the same side of the line \[y=\frac{3}{2}x-2\]as the point \[\left( 0,0 \right)\] are members of the solution set.
Since,\[y>\frac{3}{2}x-2\] is not contain an equal sign.
So, the line should be dotted.
Now, draw the graph of the equation \[y=4\]:
To draw the graph of the equation\[y=4\], draw a horizontal line with y-intercept 4.
The line is dotted because equality is not included in \[y<4\].
Because of the less than part of \[
