If A (x, 1), B (-3,7), C (-5, 9), and D (5, 4), find the value of x so that line AB is parallel to line CD.

The slope of CD = (9-4) / (-5-5) = 5/-10 = - 1/2

The slope of AB must also be - 1/2

Slope of AB = (1-7) / (x - - 3) = - 6 / (x+3)

For AB to equal - 1/2, the denominator needs to be twice as much as the numerator, so set up an equation:

2 (x+3) = 12

Now solve for x:

2x + 6 = 12

2x = 18

x = 18/2

x = 9