SOLUTION: In the North Chicago area, an 820-square-foot apartment rents for $1510 per month. A 970-square-foot apartment rents for $1660. Suppose that the relation between area and rent is l

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: In the North Chicago area, an 820-square-foot apartment rents for $1510 per month. A 970-square-foot apartment rents for $1660. Suppose that the relation between area and rent is l      Log On


   



Question 881402: In the North Chicago area, an 820-square-foot apartment rents for $1510 per month. A 970-square-foot apartment rents for $1660. Suppose that the relation between area and rent is linear.
A. Find a linear function that relates the rent, R to its area, x.
B. Predict the rent of a 900-square-foot apartment.
C. If the rent of an apartment is $1300 per month, how big would you expect it to be?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When you plot a graph, whatever you plot
on the vertical axis DEPENDS on what you
plot on the horizontal axis.
The INDEPENDENT variable is plotted on
the horizontal axis.
--------------------
In this case, area in square feet is
on the horizontal axis, and
the monthly rent is on the vertical axis
--------------------
Let +x+ = area of an apartment in square feet
Let +R+ = the monthly rent of an apartment
--------------------
You are given the poihnts
( 820, 1510 ) and
( 970, 1660 )
Use the point-slope formula:
+%28+R+-+1510+%29+%2F+%28+x+-+820+%29+=+%28+1660+-+1510+%29+%2F+%28+970+-+820+%29+
+%28+R+-+1510+%29+%2F+%28+x+-+820+%29+=+150+%2F+150+
+%28+R+-+1510+%29+%2F+%28+x+-+820+%29+=+1+
+R+-+1510+=+x+-+820+
(A)
+R+=+x+%2B+690+
--------------------
check:
( 820, 1510 )
+1510+=+820+%2B+690+
+1510+=+1510+
OK
-------------------------
(B)
+x+=+900+
+R+=+x+%2B+690+
+R+=+900+%2B+690+
+R+=+1590+
The rent is $1,590
-------------------------
(C)
+R+=+x+%2B+690+
+1300+=+x+%2B+690+
+x+=+610+
The area is 610 square feet