SOLUTION: The average daily cost of a room at a city hospital has risen by $59.82 per year for the years 1990- 2000. If the average cost of a room in 1996 was $1128.50, determine the slope

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: The average daily cost of a room at a city hospital has risen by $59.82 per year for the years 1990- 2000. If the average cost of a room in 1996 was $1128.50, determine the slope      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 676074: The average daily cost of a room at a city hospital has risen by $59.82 per year for the years 1990-
2000. If the average cost of a room in 1996 was $1128.50, determine the slope-intercept form of
the line, complete the chart, and graph it.
Whats formula could I use to make it work on excel for the years? Thank you
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
THE SLOPE-INTERCEPT FORM OF THE EQUATION FOR THE LINE:
y= cost of a room at a city hospital (in $)
x= year
(NOTE: There are other, popular alternate options, such as making x=years after 1990)
The slope-intercept form of the line would be y=mx%2Bb
where m is the slope, and b is the y-intercept.
The slope of the line for the years 1990-2000 is 59.82,
the increase of the cost (in $) per year.
You are given one point in the line, (1996,1128.5),
the point with x=1996 and y=1128.5.
For any other point within the years 1990-2000,
you would be x-1996 years after 1996,
and the cost would have increased by y-1128.5.
Since the cost increased by $59.82 per year,
y-1128.5=59.82%28x-1996%29.
That equation is in the point-slope form, using the given point and slope.
With a little algebra, we can transform it into the one and only slope-intercept form:
y-1128.5=59.82%28x-1996%29 --> y-1128.5=59.82x-59.82%2A1996 --> y-1128.5=59.82x-119400.7 --> y-1128.5%2B1128.5=59.82x-119400.7%2B1128.5 --> highlight%28y=59.82x-118272.2%29
IF you set x= year, the slope-intercept form of the line is
highlight%28y=59.82x-118272.2%29

NOTE:
IF you set x= years after 1990, the point-slope form of the line
would be y-1128.5=59.82%28x-6%29 (using point (6,1128.5))
and the slope-intercept form of the line would be
highlight%28y=59.82x%2B770.58%29

USING EXCEL FOR THE GRAPH:
If you are familiar with Excel, you will understand what I mean.
If not, maybe another way of graphing will work better.
You could use one of the equations above to generate an Excel table and graph,
but if you know Excel, you can generate everything without knowing algebra.
To use Excel for the graph I would make two columns titled x and y (A1=x, B1=y),
I would fill the x values below the x title (in the A column).
(You could use 1990, 1991, 1992, ...., if using x= year,
or 0, 1, 2, ...., if using x= years after 1990)
I would enter the value 1128.5 (B8), for the cost for 1996, in the y column,
next to the corresponding year value for the x (A8=1996 or 6).
Next, I would enter formulas above and below that 1128.5,
refering to that cell containing that value (relative reference, as in B9=B8+59.82),
so that the y value (B9) for the year 1997 (A9=1997 or 7) would be 1128.5+59.82,
and the value for 1995 would be 1128.5+59.82.
Then I would propagate the formula down for years 1997-2000 and up for years 1995-1900.