SOLUTION: In my math book the directions say ; Write an equation for a linear function f that has the given values. Example number 24 ; f(-2)=-2, f(4)=-8 I dont understand how to do this, c

Algebra ->  College  -> Linear Algebra -> SOLUTION: In my math book the directions say ; Write an equation for a linear function f that has the given values. Example number 24 ; f(-2)=-2, f(4)=-8 I dont understand how to do this, c      Log On


   

Question 686822: In my math book the directions say ; Write an equation for a linear function f that has the given values. Example number 24 ; f(-2)=-2, f(4)=-8
I dont understand how to do this, could you explain it step by step & why? Thank you.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
+f%28-2%29+=+-2+
+f%284%29+=+-8+
------------
A linear equation will have the form
+f%28x%29+=+m%2Ax+%2B+b+
+f%28-2%29+=+m%2A%28-2%29+%2B+b+
(1) +-2+=+m%2A%28-2%29+%2B+b+
-------------------
+f%284%29+=+m%2A4+%2B+b+
(2) +-8+=+m%2A4+%2B+b+
-----------------
Now I have 2 equations with
2 unknowns, so it's solvable
(1) +-2+=+m%2A%28-2%29+%2B+b+
(1) +-2m+%2B+b+=+-2+
and
(2) +-8+=+m%2A4+%2B+b+
(2) +4m+%2B+b+=+-8+
-------------------
Subtract (1) from (2)
(2) +4m+%2B+b+=+-8+
(1) +-%28-2m%29+-+b+=+-%28-2%29+
+6m+=+-6+
+m+=+-1+
and
(1) +-2m+%2B+b+=+-2+
(1) +-2%2A%28-1%29+%2B+b+=+-2+
(1) +2+%2B+b+=+-2+
(1) +b+=+-4+
The function is:
+f%28x%29+=+-x+-+4+
---------------
check answer:
+f%28-2%29+=+-%28-2%29+-+4+
+f%28-2%29+=+-2+
OK
+f%284%29+=+-4+-+4+
+f%284%29+=+-8+
OK