Part A:
It depends on the signs:
The line is solid if:
The inequality involves a greater equal or a lesser equal.
example:
[tex]\begin{gathered} x+y\ge1 \\ or \\ x+y\le1 \end{gathered}[/tex]The line is dashed if:
Inequality involves a greater than or less than.
example:
[tex]\begin{gathered} 5x+2<10 \\ or \\ 5x+2>10 \end{gathered}[/tex]This is because when we speak of a strict greater or lesser. the area does not touch the boundary line. While in the opposite case if it touches the border line.
Part B:
Let's evaluate the point (x,y) = (0,0):
[tex]\begin{gathered} 3x+y>4 \\ x=0,y=0 \\ 0+0>4 \\ 0>4 \\ This_{\text{ }}is_{\text{ }}false \\ 0<4 \end{gathered}[/tex]We can conclude that this point is not a solution for the inequality, so, it does not belong to the solution region:
Part C:
Let's focus on graph the equivalent line:
[tex]\begin{gathered} y=2x-1 \\ \end{gathered}[/tex]From this equation we can see:
[tex]\begin{gathered} m=2 \\ b=-1 \\ y-\text{intercept}=(0,-1) \\ x-\text{intercept}=(0.5,0) \end{gathered}[/tex]since it is greater than (>), the line is dashed and the shaded region is above the line:
