SOLUTION: Two parallel lines y=-2x+2 and y=-2x-3 are intersected by a transversal with slope 1/2 which crosses the y axis at 2. What is the distance between the two points where the transver

Question 179846: Two parallel lines y=-2x+2 and y=-2x-3 are intersected by a transversal with slope 1/2 which crosses the y axis at 2. What is the distance between the two points where the transversal intersects the parallel lines?
Answer by HyperBrain(694) (Show Source): You can put this solution on YOUR website!
The transversal has slope 1/2 and passes through (0,2)[y-intercept].So,
y-2=x/2
2y-4=x
x=2y-4
Subtituting this to y=-2x+2,
y=-2(2y-4)+2
y=(-4y+8)+2
y=-4y+10
5y=10
y=2
x=2y-4=2(2)-4=4-4=0 The point of intersection is (0,2)
Substituting x=2y-4 to y=-2x-3,
y=-2(2y-4)-3
y=(-4y+8)-3
y=-4y+5
5y=5
y=1
x=2y-4=2(1)-4=2-4=-2 The point of intersection is (-2,1)
The distance between (0,2) and (-2,1)

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