1. Take an arbitrary point that lies on the first line y=3x+10. Let x=0, then y=10 and point has coordinates (0,10).
2. Use formula [tex] d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}} [/tex] to find the distance from point [tex] (x_0,y_0) [/tex] to the line Ax+By+C=0.
The second line has equation y=3x-20, that is 3x-y-20=0. By the previous formula the distance from the point (0,10) to the line 3x-y-20=0 is:
[tex] d=\dfrac{|3\cdot 0-10-20|}{\sqrt{3^2+(-1)^2}}=\dfrac{30}{\sqrt{10}}=3\sqrt{10} [/tex].
3. Since lines y=3x+10 and y=3x-20 are parallel, then the distance between these lines are the same as the distance from an arbitrary point from the first line to the second line.
Answer: [tex] d=3\sqrt{10} [/tex].
