Two straight lines are given by the equations y = 2x + 3 and y = -3 + 2. Find the angle between these straight lines.

1. The slope of a straight line is equal to the tangent of the angle between this straight line and the positive direction of the abscissa axis:

a) y = 2x + 3;

k = 2;

tgα = 2;

b) y = -3x + 2;

k = -3;

tgβ = -3.

2. Find the difference in angles between the straight lines γ = | α – β |:

tgγ = | tg (α – β) |;
tgγ = | (tgα – tgβ) / (1 + tgα * tgβ) |;
tgγ = | (2 – (-3)) / (1 + 2 * (-3)) |;
tgγ = | (2 + 3) / (1 – 6) |;
tgγ = | 5 / (- 5) |;
tgγ = 1.
γ = π / 4.
Answer. The angle between the straight lines is 45 °.