The line perpendicular to both of this lines has a slope of -1/3 and the length of a segment of it, which is between two those lines, gives the distance between them. Let us consider the line y=-x/3. It is perpendicular to both lines. It intercepts y=3x+4 at the point, which x-coordinate satisfies the following equation:
-x/3=3x+4; or x=-6/5=-1.2; y-coordinate is y=-1.2/-3=0.4
Analogously, it intercepts the line 3x-6 at x=1.8
-x/3=3x-6 x=9/5=1.8
y-coordinate is 1.8/-3=-0.6
Distance between two lines, 3x+4 and 3x-6, is:
d=√[(1.8-(-1.2))^{2}+(-0.6-0.4)^{2}]=√(3^{2}+(-1)^{2})=√10
Answer: √10
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