I don't know how to find the slope of a line that's the angle bisector of two lines using slope-intercept form, could somebody help me?
The lines \(y = \frac{1}{3} x\) and \(y = \frac{13}{9} x\) are drawn in the coordinate plane. Find the slope of the line that bisects the angle between these lines.
Let a be the angle betwen the line y = 1/3*x and the x-axis, and let b be the angle betwen the line y = 13/9*x and the x-axis. Then tan(a) = 1/3 and tan(b) = 13/9, so a = arctan(1/3) and b = tan(13/9).
The angle for the angle bisector is (a+ b)/2, and tan((a + b)/2) = (13/9 + 1/3)/(1 + 13/9*1/3) = 6/5.
So, the slope of the angle bisector is 6/5.
