2, 4, -2,-2
1) Examining the graph, let's write down the coordinates of each of those points:
M(-2,0) M' (6,-4)
N (-6,8) N' (2,4)
2) Picking the points as a reference, we can answer those questions. We can see that the line MN was translated 2 units down (Note the position from M and M').
And MN was also translated to the right 4 units.
3) We are going to need to make use of the slope formula to get the slope of MN:
[tex]m_{MN}=\frac{y_2-y_1}{x_2-x_1}=\frac{8-0}{-6-(-2)}=\frac{8}{-6+2}=\frac{8}{-4}=-2[/tex]Note that we are considering the coordinates of M and N for this calculation.
And likewise, for the M'N' (the transformed line) we've got:
[tex]m_{M^{\prime}N^{\prime}}=\frac{4-(-4)}{2-6}=\frac{8}{-4}=-2[/tex]Notice that since the slope of MN and M'N' are the same, then we can verify that these are parallel lines.
4) Thus the answers are:
[tex]\begin{gathered} a)2 \\ b)4 \\ -2 \\ -2 \end{gathered}[/tex]