SOLUTION: Two lines with slopes 3 and -4 intersect at a point P on the y-axis.If their x-intercepts are 14 units apart, find the distance of P from the origin.

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Question 1151104: Two lines with slopes 3 and -4 intersect at a point P on the y-axis.If their x-intercepts are 14 units apart, find the distance of P from the origin.
Answer by greenestamps(13203) About Me  (Show Source):
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Call the coordinates of point P (0,b).

Find the x intercept of a line with slope 3 passing through P(0,b):

%28b-0%29%2F%280-x%29+=+3
b%2F%28-x%29+=+3
b+=+-3x
x+=+%28-1%2F3%29b

Find the x intercept of a line with slope -4 passing through P(0,b):

%28b-0%29%2F%280-x%29+=+-4
b%2F%28-x%29+=+-4
b+=+4x
x+=+%281%2F4%29b

Use the fact that the two x-intercepts are 14 units apart to determine b.

%281%2F4%29b-%28-1%2F3%29b+=+14
%281%2F4%29b%2B%281%2F3%29b+=+14
%287%2F12%29b+=+14
b+=+%2812%2F7%29%2A14+=+12%2A2+=+24

ANSWER: The distance of P from the origin is b = 24.