SOLUTION: The line x+3y=_2 and x+3y=8 are parallel .find the distance between them

Question 1053876: The line x+3y=_2 and x+3y=8 are parallel .find the distance between them
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!

Make a perpendicular to the line that has an x-intercept of 8, or (8,0). It has a slope of 3 (negative reciprocal). The equation of that line is y=3x-24, using the point slope formula of y-y1=m(x-x1)=3(x-8)
Find where it intersects the other line with equation y=(-x/3)+(2/3).
Now write both in standard form and solve
-3x+y=-24
x+3y=2
3x+9y=6, multiplying by 3
10y=-18
y=-1.8
substitute into the second equation and x-5.4=2
x=7.4
Check in the first: -22.2-1.8=-24
So, we want the distance between (7.4,-1.8) and (8,0)
sqrt(1.8^2+0.36)=sqrt(3.6)=1.897 or 1.9 units
RELATED QUESTIONS
How do you find the distance between x+3y=6 and x+3y=-14 if they are both parallel... (answered by solver91311)

Find the distance between the given line 4x - 3y = 12 and 4K 3y + 8 =... (answered by ikleyn)

Find the distance between the given line 4x - 3y = 12 and 4x - 3y + 8 =... (answered by ikleyn)

Find the equation of the line parallel to the line x-3y=2 and passing at a distance... (answered by josgarithmetic)

Find the equation of the line parallel to the line x-3y=2 and passing at a distance... (answered by josgarithmetic,josmiceli)

Find the distance between the $x$-intercept and the $y$-intercept of the line below.... (answered by mccravyedwin,math_tutor2020)

find the distance between each pair of parallel lines x+3y=-14 (answered by sophmore)

find the distance between the pair of parallel lines y=x-6 and y=x+8 (answered by Alan3354)

Find the equation of a line that is parallel to x + 3y = 2 and containing the point (0,... (answered by mananth)