Find the angle between the lines

Question

x-3y+5=0 & 2x-3y-7= 0?

 

A) 30 degree
B) 45 degree
C) 90 degree
D) 0 degree

 

Answer 1

The lines are 2x - 3y + 5 = 0 and 2x - 3y - 7 = 0

Write the two lines in slope intercept form y = mx + b.

• First line 2x - 3y + 5 = 0

2x + 5 = 3y

y =  2x/3 + 5/3

First line slope is 2/3.

• Second line 2x - 3y - 7 = 0

3y = 2x - 7

y = 2x/3 - 7/3

Second line slope is 2/3.

The two lines slopes are equal.

So 2x - 3y + 5 = 0 and 2x - 3y - 7 = 0 are parallel lines.

parallel lines does not intersect.

Therefore angle between 2x - 3y + 5 = 0 and 2x - 3y - 7 = 0 is zero.

Option D is correct choice.