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

Answer:

            Only:  C.  The lines are perpendicular.

Step-by-step 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