SOLUTION: Find the distance between 3x-y+5=0 and 6x-2y-7=0.

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Question 672537: Find the distance between 3x-y+5=0 and 6x-2y-7=0.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
3x-y%2B5=0 and 6x-2y-7=0

3x%2B5=y
6x-7=2y...=>..3x-3.5=y
+graph%28+600%2C600%2C+-10%2C+10%2C+-10%2C+10%2C+3x%2B5%2C+3x-3.5%29+
now use distance formula and find the distance between one point on
3x%2B5=y and one on 3x-3.5=y

easiest way is to find x-intercept or y-intercept
let use x-intercept because lines are parallel and slopes are positive
and find x-intercepts

3x%2B5=y....=>....3x%2B5=0..=>..3x=-5..=>..x=-5%2F3...=>..x=-1.17
x-intercept is at (-5%2F3,0)

3x-3.5=y....=>....3x-3.5=0..=>..3x=3.5..=>..x=1.17..=>.x-intercept is at (1.17,0)

find the distance (note the distance between these two points is equal to the distance between given two lines)

Solved by pluggable solver: Distance between two points in two dimensions
The distance (denoted by d) between two points in two dimensions is given by the following formula:

d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%281.17--1.17%29%5E2+%2B+%280-0%29%5E2%29=+2.34+


For more on this concept, refer to Distance formula.