SOLUTION: The line y=-12/5x+2 is exactly 3 units away from the other two lines parallel to it. The distance, in units, between the y-intercepts of these two other lines is

Algebra ->  Points-lines-and-rays -> SOLUTION: The line y=-12/5x+2 is exactly 3 units away from the other two lines parallel to it. The distance, in units, between the y-intercepts of these two other lines is       Log On


   

Question 1064758: The line y=-12/5x+2 is exactly 3 units away from the other two lines parallel to it. The distance, in units, between the y-intercepts of these two other lines is
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can form a right triangle with the spacing between lines and the distance between the intercepts.
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You can form another triangle with the line and the y axis using the slope of the line. The angles shown then have a relationship.
tan%28A%29=12%2F5
A%2BB=90
cos%2890-B%29=3%2FY
cos%28A%29=3%2FY
So then,
Y=3%2Fcos%28A%29
and
cos%28A%29=5%2Fsqrt%285%5E2%2B12%5E2%29=5%2F13
Then,
Y=3%2F%285%2F13%29
highlight%28Y=39%2F5%29