SOLUTION: The equations of three lines are given below: Line 1: 4y = 3x + 5 Line 2: y = 3/4x + 8 Line 3: 8x - 6y = -6 For each pair of lines, determine whether they are parallel,

Algebra ->  Expressions-with-variables -> SOLUTION: The equations of three lines are given below: Line 1: 4y = 3x + 5 Line 2: y = 3/4x + 8 Line 3: 8x - 6y = -6 For each pair of lines, determine whether they are parallel,      Log On


   



Question 1153686: The equations of three lines are given below:
Line 1: 4y = 3x + 5
Line 2: y = 3/4x + 8
Line 3: 8x - 6y = -6
For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2.
Line 1 and Line 3.
Line 2 and Line 3.

Thank you so much!!

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let's write all three equations in the form y = ax + b.


Line 1:  y = %283%2F4%29x + 5%2F4


Line 2:  y = %283%2F4%29x + 8


Line 3:  y = %284%2F3%29x + 1.



Now you see that Line 1 and Line 2 have the same slope, but they are not identical; they are different. 

    Hence, they are parallel.



Line 1 and Line 3 have different slope; hence, they are not parallel.

The slopes  {{3/4}}} and  4%2F3 are not negative reciprocal. Hence, Line 1 and Line 2 are not perpendicular.

    The optional answer is NEITHER.



Line 2 and Line 3 have different slope; hence, they are not parallel.

The slopes  {{3/4}}} and  4%2F3 are not negative reciprocal. Hence, Line 2 and Line 3 are not perpendicular.

    The optional answer is NEITHER.


Solved. // All questions are answered.