Find the point of intersection and the angle between y=5x-2 and y=3x+6. Use absolute (positive) value of the angle.

Question

point of intersection is (_, _)

angle of intersection is _ degrees (round-off to 2 decimal places)

Answer 1

Point of intersection is when 5x-2=3x+6, 2x=8, x=4, so y=5x-2=18=3x+6. The point is (4,18).

The angle between them θ is given by the triangle rule that the external angle of a triangle is the sum of the two opposite interior angles, so arctan(5)=θ+arctan(3) where 5 and 3 are the slopes of the two lines.

So θ=arctan(5)-arctan(3)=7.12° approx. (The difference between 78.69° and 71.565°)