Step: 1
Two lines which have the same slope and different y-intercepts are called parallel lines.
Step: 2
Write all the sets of equations in the standard slope-intercept form, y = mx + b and verify.
Step: 3
For the lines -x + 53y + 3 = 0, x - 53y - 4 = 0:
Step: 4
-x + 53 y + 3 = 0 ⇒ y = 35 x - 9/5
Step: 5
Slope =
35and
y-intercept = -
95
[Compare with y = mx + b.]
Step: 6
x - 53y - 4 = 0 ⇒ y = 35 x - 125
Step: 7
Slope =
35 and
y-intercept = -
125 [Compare with y = mx + b.]
Step: 8
Slopes are same and y-intercepts are different.
Step: 9
So, -x + 5/3 y + 3 = 0, x - 5/3 y - 4 = 0 are parallel.
Correct Answer is : -x + 53y + 3 = 0, x - 53 y - 4 = 0