Question

identify which lines are parallel: y= -1/2x +3, y=1/2x+1, y=2x, x+2y=4

Answer 1

Standerd form of slope intercept form y = mx+b

Here m =slope and b = y intercept

Given equations say L1,L2,L3,L4 and thier slopes are say m1,m2,m3,m4 .

L1 ⇒ y = -1/2x+3

Compare it to standerd form then m1 = -1/2.

L2 ⇒ y = 1/2x+1

Compare it to slope intercept form then m2 = 1/2.

L3⇒ y = 2x

Compare it to slope intercept form then m3 =2

L4⇒ x+2y = 4

Subtract x from each side.

x-x+2y = 4-x

2y = 4-x

Divide to each side by 2.

2y/2 = (4-x)/2

y = 2-x/2

y = (-1/2)x+2

L4 slope is m4 = -1/2

We know that parallel lines slopes are always equal.

m1 = m4

So the lines y = -1/2x+3 and x+2y = 4 are parallel to each other.