SOLUTION: Dear Math Tutor, The curve y=1+1/(2+x) crosses the x-axis at the point A and the y-axis at the point B. a) Calculate the coordinates of A and B b) Find the equation of line AB

Algebra ->  Coordinate-system -> SOLUTION: Dear Math Tutor, The curve y=1+1/(2+x) crosses the x-axis at the point A and the y-axis at the point B. a) Calculate the coordinates of A and B b) Find the equation of line AB      Log On


   

Question 871197: Dear Math Tutor,
The curve y=1+1/(2+x) crosses the x-axis at the point A and the y-axis at the point B.
a) Calculate the coordinates of A and B
b) Find the equation of line AB
c) Calculate the coordinates of the point of intersection of the line AB and the line with equation 3y=4x
For a) Do I use: y=mx+b and does mx=1 and b=1/(2+x)?
With Gratitude,
Nats
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

0 = 1 + 1/(2+x)

-1 = 1/(2+x)

 x = -3   

A = (-3,0)

y = 1+1/2  when x = 0

B = (0, 1.5)

c) Calculate the coordinates of the point of intersection of the line AB and the line with equation 3y=4x   0r y+=+%284%2F3%29x

B(0, 1.5)

A(-3 ,0) m = 1.5/3 = 1/2

Line AB

 y - 0 = (1/2)(x+3)   ***Using point-slope form, y+-+y%5B1%5D+=+m%28x+-+x%5B1%5D%29P(-3,0)

 y+=+%281%2F2%29x+%2B+3%2F2  Line AB

 Calculating the coordinates of the point of intersection line AB and line y+=+%284%2F3%29x

%284%2F3%29x+=+%281%2F2%29x+%2B+3%2F2

     8x = 3x + 9

     5x = 9

      x = 9/5 = 1.8  and y = 36/15 = 12/5 = 2.4

(1.8, 2.4) Point of Intersection