so if a slope of two lines is 4/a and -7, determine the value of a if the lines are parallel, and if they are perpendicular.

Parallel means the slope is the same so 4/a = -7 solve for 'a'

Perpindicular means one slope is -1/other

so 4/a = - 1/-7

4/a = 1/7 solve for 'a'

yes i understood that far, but what is the solution to a?

You SHOULD know how to solve for 'a' given:

4/a = -7 multiply both sides by a

4 = -7a divide both sides by 7

-4/7 = a

You should do the second one......