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.