Question 916844
Two lines are parallel if their SLOPES are equal.
The slope of a line is (difference in the y coordinates}/(difference in the x coordinates).
The slope of the first line is (11-7)/(5-(-3)) or 4/8 or 1/2
The slope of the second line is (k-5)/(-2-2) or (k-5)(-4).
Now set the slopes equal to each other to get
(k-5)(-4) = 1/2 or
(k-5) =(-4)/2 or
k = 5 - 2 or
k = 3
Let's check this.
Is ((3-5)/(-4) = 1/2)?
Is (-2/(-4) = 1/2)?
Is (1/2 = 1/2)? Yes
Answer: When k = 3 the lines are parallel.