SOLUTION: I am to find the values of a and b, having been given two points. Coordinates (-2,-6) and (1,-3) Using the form y=(a/x)+b Should I be using simultaneous equations?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I am to find the values of a and b, having been given two points. Coordinates (-2,-6) and (1,-3) Using the form y=(a/x)+b Should I be using simultaneous equations?      Log On


   

Question 1024026: I am to find the values of a and b, having been given two points.
Coordinates (-2,-6) and (1,-3)
Using the form y=(a/x)+b
Should I be using simultaneous equations?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Do you WANT to use simultaneous equations? You can.

Your chosen form, y=%28a%2Fx%29%2Bb.

Substituting the x and y coordinates to form two equations for the system:system%28-6=a%2F%28-2%29%2Bb%2C-3=a%2F1%2Bb%29

Simplify the system:
system%28-6=-a%2F2%2Bb%2C-3=a%2Bb%29

system%28-12=-a%2B2b%2C-3=a%2Bb%29

a-12=2b
highlight_green%28a=2b%2B12%29-----You will use this again later...
substitute into the other equation.
-3=%282b%2B12%29%2Bb
-3=2b%2B12%2Bb
-3=3b%2B12
-1=b%2B4
-1-4=b
highlight%28b=-5%29

Find a.
a=2b%2B12
a=2%28-5%29%2B12
a=-10%2B12
highlight%28a=2%29

Finishing with your chosen form,
highlight%28y=2%2Fx-5%29