**Solution: **

The line passing through the point=(4,5)

The line equally inclined to the lines 3x=4y+7,5y=12x+6 means the angle between the required line and the two lines is equal assume the slop of the required equation is m1

The slope of the equation 3x=4y+7=>y=(3x)/4-7/4 so the slope of the equation is ¾

The slope of the equation 5y=12x+6=>y=(12x)/5+6/5 so the slope of the equation is 12/5

When slope of the two equations are formula for finding the angle between them is

a=tan^{-1}(m1-m2)/1+m1m2=tan^{-1}(m1-m2)/1+m1m2

=tan^{-1}(m1-3/4)/1+3m1/4=tan^{-1}(m1-12/5)1+12m1/5)

=>(4m1-3)/(4+3m1)=(5m1-12)/(5+12m1)

=>(20m_{1}+48m_{1}^{2}-15-36m_{1}=20m_{1}+15m_{1}^{2}-48-36m_{1})

=>m_{1}^{2}=1

=>m_{1}=+1 or -1

so the two equations incline the given ttwo equations equally

those are passing throught he point (4,5) and having the slope 1 and -1

**Those are y-x+1=0 and y+x-9=0**