Answer to Question #162884 in Algebra for Jefferson Morales

Question

1. Determine whether the lines given by the equations below are parallel, perpendicular, or neither. Also, find a rigorous algebraic solution for each problem.

Answer 1

a)

3y + 4x = 12, has slope -4/3

-6y = 8x+1 has slope -8/6 = - 4/3

the slopes are the same so the lines are parallel

b) 3y +x = 12, has slope -1/3

y = 8x+1 has slope 8

the slopes are different, not negative reciprocals,

so the lines are neither parallel nor perpendicular;

they will intersect at a unique point

c) 4x - 7y = 10 , has slope 4/7

7x + 4y = 1 has slope -7/4

the slopes are negative reciprocals, so the lines are

perpendicular