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.

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. 

To Find: The equation of the line? 

The formula used: The equation of the line is y = mx + c 

Explanation: 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) 

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

y = 3x – 4 

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