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.