Endpoints of segment MN have coordinates (0, −3), (−2, −4). Endpoints of segment AB have coordinates (2, 5), (4, k). What value of k makes these segments parallel?

Answer:The value of k is 6Step-by-step explanation:we know thatIf two segments are parallel, then their slopes are the samewe know that The formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] step 1 Find the slope MNwe haveM(0, −3), N(−2, −4)substitute[tex]m=\frac{-4+3}{-2-0}[/tex] [tex]m=\frac{-1}{-2}[/tex][tex]m=0.5[/tex] step 2Find the slope ABA(2, 5), B(4, k)substitute in the formula[tex]m=\frac{k-5}{4-2}[/tex] [tex]m=\frac{k-5}{2}[/tex] Remember that the slopes MN and AB must be equal[tex]0.5=\frac{k-5}{2}[/tex]Solve for k[tex]1=k-5[/tex][tex]k=1+5=6[/tex]thereforeThe value of k is 6