Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.

Let the slope of the required line be m₁.

The given line can be written as , which is of the form y = mx + c

∴Slope of the given line =

It is given that the angle between the required line and line x – 2y = 3 is 45°.

We know that if θisthe acute angle between lines l₁ and l₂ with slopes m₁ and m₂ respectively, 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 =

The equation of the line passing through (3, 2) and having a slope of is:

Thus, the equations of the lines are 3x – y = 7 and x + 3y = 9.