Why is the slope tangent to the tilt angle Today, I learned that the coefficient of the linear equation directly affects the inclination angle of the line in the coordinates, and then the coefficient can be calculated through the tangent of the inclination angle. Well, it can be calculated in this way, but why? What's the principle? Please tell me in detail. Thank you

Why is the slope tangent to the tilt angle Today, I learned that the coefficient of the linear equation directly affects the inclination angle of the line in the coordinates, and then the coefficient can be calculated through the tangent of the inclination angle. Well, it can be calculated in this way, but why? What's the principle? Please tell me in detail. Thank you

Because the slope is Y / X and the tangent of the tilt angle is Y / X

After two points a (- m, 6), B (M + 1,3m), the tangent of the inclination angle of the straight line is 2, and the value of M is obtained

(3m-6)/(m+1+m)=2
3m-6=4m+2
m=-8

The tangent of the inclination angle of the line PQ passing through points P (2,3) and Q (1,5) is______ ．

∵ the point P coordinate is (2,3), and the point Q coordinate is (1,5) ∵ the slope of the line PQ is k = 5 − 31 − 2 = - 2. If the inclination angle of the line is α, then Tan α = - 2, so the answer is: - 2