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Question 1188641: Find the equation of the line whose slope is 3/2 and which passes through P, where P divides the line segment joining A(-2,6) and B(3,-4) in the ratio 2:3 internally.
Answer by greenestamps(13215)   (Show Source):
You can put this solution on YOUR website!
Technically the statement of the problem is insufficient -- we don't know for sure whether the ratio 2:3 is AP:PB or BP:PA.
I will guess that AP:PB = 2:3.
From A to B is a change of +5 in the x direction and -10 in the y direction.
P is (2/(2+3)) = 2/5 of the way from A to B.
2/5 of 5 is 2; 2/5 of -10 is -4.
The x coordinate of P is -2+2=0; the y coordinate is 6+(-4)=2.
So we have a line through (0,2) with slope of 3/2. Since (0,2) is the y-intercept, you can plug the values directly into the slope-intercept form of the equation.
y = mx+b
y = (3/2)x+2
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