Question

The equations of three lines are given below.

Line 1: y = -5/2x+6
Line 2: 2y = -5x+5
Line 3: 10x+4y= -4

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:

Answer 1

all parallel

Explanation:

to see it very clearly, we need to bring each equation to a "y = ..." form.

because then the factor of x will tell us precision the slope of every line.

the same slope means parallel, the slope fraction upside-down with switched sign means perpendicular, anything else means neither.

line 1 : y = (-5/2)x + 6

line 2 : 2y = -5x + 5

y = (-5/2)x + 5/2

line 3 : 10x + 4y = -4

4y = -10x - 4

y = (-10/4)x - 1 = (-5/2)x - 1

so, all 3 lines have the same slope (-5/2) and are therefore parallel to each other.

a perpendicular slope (90°) would have been

2/5

with the slope fraction upside-down and the sign flipped.

any other slope would have meant "neither".