Find the equation of a line which makes an angle of tan– 1 (3) with

1.	Find the equation of a line which makes an angle of tan– 1 (3) with the x–axis and cuts off an intercept of 4 units on the negative direction of y–axis.
Answer» Given: The equation which makes an angle of tan^{– 1}(3) with the x–axis and cuts off an intercept of 4 units on the negative direction of y–axis By using the formula, The equation of the line is y = mx + c Here, angle θ = tan^{– 1}(3) So, tan θ = 3 The slope of the line is, m = 3 And, Intercept in the negative direction of y–axis is (0, -4) The required equation of the line is y = mx + c Now, substitute the values, we get y = 3x – 4 ∴ The equation of the line is y = 3x – 4.

Find the equation of a line which makes an angle of tan– 1 (3) with the x–axis and cuts off an intercept of 4 units on the negative direction of y–axis.

Answer»

Given:

The equation which makes an angle of tan^{– 1}(3) with the x–axis and cuts off an intercept of 4 units on the negative direction of y–axis

By using the formula,

The equation of the line is y = mx + c

Here, angle θ = tan^{– 1}(3)

So, tan θ = 3

The slope of the line is, m = 3

And, Intercept in the negative direction of y–axis is (0, -4)

The required equation of the line is y = mx + c

Now, substitute the values, we get

y = 3x – 4

∴ The equation of the line is y = 3x – 4.