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Solution :

Converting each of the given equation to the form y=mx+C, we get <br> `3x-4y+9=0 Rightarrow y=(3)/(4)x+(9)/(4)..........(i)` <br> `6x-8y+17=0 Rightarrow y=(3)/(4)x-(17)/(8)..........(ii)` <br> Clearly, the slopes of the given lines are equal and so they are parallel, <br> Let hte given line be `y=mx+C_(1) and y=mx+C_(2)"where "m=(3)/(4), C_(1)=(9)/(4) and C_(2)=(-17)/(8)` <br> `therefore` distance between given line=`(|C_(2)-C_(1)|)/(sqrt(1+m^(2)))=(|(-17)/(8)=(9)/(4)|)/(sqrt(1+(9)/(16)))=(|(-35)/(8)|)/(((5)/(4)))=((35)/(8)xx(4)/(5))=(7)/(2)"units"` <br> Hence, the distance between the given lines is `(7)/(2)` units.