Find the value of a if the line 2y - ax + 4 = 0 is perpendicular to the line y + (x/4) - 7 = 0
A.
-4
B.
4
C.
8
D.
-8
Correct Answer: 8
Explanation
2y - ax + 4 = 0 ⟹
2y = ax - 4.
y + (x/4) - 7 = 0 ⟹
y = -x/4 + 7
Slope of line 1 = a/2
Slope of line 2 = -1/4
-1/4 x a/2 = -1 (product of the slope of two perpendicular lines = -1)
a/8 = 1 ⟹
a = 8.
2y - ax + 4 = 0 ⟹
2y = ax - 4.
y + (x/4) - 7 = 0 ⟹
y = -x/4 + 7
Slope of line 1 = a/2
Slope of line 2 = -1/4
-1/4 x a/2 = -1 (product of the slope of two perpendicular lines = -1)
a/8 = 1 ⟹
a = 8.