SOLUTION: Determine the point {{{P(x, y) }}} on the graph of the equation {{{y= sqrt (x+1) }}} such that the slope of the line through the point (3, 2) and P is 3/8

Algebra ->  Graphs -> SOLUTION: Determine the point {{{P(x, y) }}} on the graph of the equation {{{y= sqrt (x+1) }}} such that the slope of the line through the point (3, 2) and P is 3/8      Log On


   

Question 1065873: Determine the point P%28x%2C+y%29+ on the graph of the equation y=+sqrt+%28x%2B1%29+ such that the slope of the line through the point (3, 2) and P is 3/8
Found 2 solutions by josgarithmetic, Boreal:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%28x%2B1%29-2%29%2F%28x-3%29=3%2F8 using formula for slope of a line

8%2Asqrt%28x%2B1%29-8%2A2=3x-9
8sqrt%28x%2B1%29=3x%2B7
64%28x%2B1%29=9x%5E2%2B42x%2B49
64x%2B64=9x%5E2%2B42x%2B49

64x=9x%5E2%2B42x-15
9x%5E2-22x-15=0
Can you continue from here for the x you need, and find y?

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Csqrt%28x%2B1%29%29
The point is (x,y). The slope is (2-y)/(3-x)=(3/8)
That is 16-8y=9-3x
or 3x+7=8y; but y = sqrt (x+1)
right side is 8 sqrt (x+1)
square both sides
9x^2+42x+49=64(x+1)=64x+64
9x^2-22x-15=0
(9x+5)(x-3)=0
x=3 (doesn't help) and x=-5/9
y is sqrt ( -5/9 +1)= sqrt (4/9) =2/3
the slope between (-5/9,2/3) and (3,2)=2-(2/3) or 12/9 divided by 3-(-5/9)=32/9
12/9 divided by 32/9 is 3/8.
The point has to be to the left of (3,2), because the derivative is 1/2 sqrt (x+1), which at x=3 gives a slope of 1/(2*2)=1/4, and the slope gets less further to the right.