Question

find angle between the lines x+3y-8=0 &2x-3y+6=0.

Answer 1

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

Given  first line x +3y -8 = 0

Subtract x  from each side.

3y -8 = -x

Add 8 to each side.

3y = -x +8

Divide to each side by 3.

y  = (-1/3)x +8/3

Second line 2x -3y +6 = 0

Subtract 2x  and 6 from each side.

-3y  = -2x -6

Divide to each side by negitive 3.

y  = (2/3)x +2

Given lines slopes are

Fromula for angle between two lines is

Substitute the above values in formula.

The angle between given lines is