Question

Which of the following is true about the lines defined by the equations 4x−2y=6 and x+2y=14? .

A.The lines share the same y-intercept.
B.Both lines intersect at point (1,−1).
C.The lines are perpendicular.
D.The lines are parallel.

Answer 1

Only: C. The lines are perpendicular.

Explanation:

4x - 2y = 6 x + 2y = 14

- 2y = - 4x + 6 2y = - x + 14

y = 2x - 3 y = - ¹/₂x + 7

A.

y-intecept: (0, -3) (0, 7)

The lines don't share the same y-intercept

B.

x=1 ⇒ y = 2(1)-3 = -1 and y = -¹/₂(1) + 7 = 6¹/₂ ≠ -1

the line x+2y=14 doesn't go through point (1,−1) so the lines couldn't intersect at point (1,−1)

Slope: m₁ = 2 m₂ = -¹/₂

C.

m₁· m₂ = 2·(-¹/₂) = -1

The lines are perpendicular.

D.

m₁ ≠ m₂ The lines are not parallel