Question

find the angle made by the line joining points (5 ,3) and( -1, - 3)
with the positive direction of x-axis​

Answer 1

angle will be pie/4 or 45°

Answer 2

The GIVEN equation

y = -3x - 2

is in the standard slope-intercept form of

y = mx + b

where

m = slope

b = y-intercept

Comparing the given equation with the standard form, the slope "m" is equal to -3.

NOTE that

tan Θ = m = slope

where

Θ = angle that the line makes with the horizontal

This being said,

tan Θ = -3

Θ = arc tan -3

Θ = -72 degrees (rounded off to the nearest degree)

The tangent of an angle is NEGATIVE in the second and fourth quadrants. It the angle is located in the second quadrant, then its values is 108 degrees (180 - 72) measured counterclockwise from the x- axis in the first quadrant.

I will leave it up to you (for your mental exercise) to figure out the value of the angle if it is located in the fourth quadrant.

hope this answer helpful u