Let the slope of the required line be m1.
The given line can be written as y=1/2 x-3/2 which is of the form y = mx + c
Slope of the given line = m2 =1/2
It is given that the angle between the required line and line x – 2y = 3 is 45°.
We know that if θ is the acute angle between lines l1 and l2 with slopes m1 and m2 , then
Case I: m1 = 3
The equation of the line passing through (3, 2) and having a slope of 3 is:
y – 2 = 3 (x – 3) y – 2 = 3x – 9
3x – y = 7
Case II: m1 = 1/3
The equation of the line passing through (3, 2) and having a slope of -1/3 is :
Thus, the equations of the lines are 3x – y = 7 and x + 3y = 9.
