SOLUTION: Let y (# dollars in your bank account) be a linear equation of x (# years since 1980). If you had $2500 in your account in 1986 and $4500 in 1994: A. Write y as a function of x

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Let y (# dollars in your bank account) be a linear equation of x (# years since 1980). If you had $2500 in your account in 1986 and $4500 in 1994: A. Write y as a function of x       Log On


   



Question 824968: Let y (# dollars in your bank account) be a linear equation of x (# years since 1980). If you had $2500 in your account in 1986 and $4500 in 1994:
A. Write y as a function of x
B- how much were you saving each year?
C- how much will you have in 2006?

---I've tried many ways of doing this, but right now I am completely lost. Thank You!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The key is that it is a linear, or straight line
equation.
-------------
(A)
If you are plotting y on the vertical axis
and x on the horizontal axis, then
you are given 2 points:
( 6, 2500 ) and ( 14, 4500 )
Note that 6 and 14 are years since 1980
----------------------------------
Use the general point-slope equation:
+%28+y+-+2500+%29+%2F+%28+x+-+6+%29+=+%28+4500+-+2500+%29+%2F+%28+14+-+6+%29+
+%28+y+-+2500+%29+%2F+%28+x+-+6+%29+=+2000+%2F+8+
+%28+y+-+2500+%29+%2F+%28+x+-+6+%29+=+250+
+y+-+2500+=+250%2A%28+x+-+6+%29+
+y+=+250x+-+1500+%2B+2500+
+y+=+250x+%2B+1000+
--------------------
(B)
In the first year,
change in y is
+y%281%29+-+y%280%29+=+1250+-+1000+
+250+
$250 is saved each year
--------------------
(C)
In 26 years, you will have:
+y+=+250%2A26+%2B+1000+
+y=+6500+%2B+1000+
+y+=+7500+
$7,500
--------
check:
does the line go through ( 6, 2500 ) and ( 14, 4500 ) ?
( 6, 2500 )
+y+=+250x+%2B+1000+
+2500+=+250%2A6+%2B+1000+
+2500+=+1500+%2B+1000+
+2500+=+2500+
OK
+y+=+250x+%2B+1000+
+4500+=+250%2A14+%2B+1000+
+4500+=+3500+%2B+1000+
+4500+=+4500+
OK