y = ax + b,
if the slope of the line is 1, what is the acute angle between the line and the x-axis?
The slope of the line is 1, so a=1.
Since the slope of a line equals the tangent of the angle between the x-axis and the line, we find that:
tan(angle) = 1
So if we take the arctangent (which is the inverse of the tangent function) of 1, we find that the angle must equal 45°.