precalc
posted by bennett on .
The table shows the closing value of a stock index for one week in March, 2004.
a. Using the day as the xvalue and the closing value as the yvalue, write equations in slopeintercept form for the lines that represent each value change.
b. What would indicate that the rate of change for two pair of days was the same? Was the rate of change the same for any of the days shown?
c. Use each equation to predict the closing value for the next business day (Day 22). The actual closing value was 1909.90. Did any equation correctly predict this value? Explain.
Stock Index
March, 2004
______________________
Day  Closing Value
15  1939.20
16  1943.09
17  1976.76
18  1962.44
19  1940.47

for each pair do
y = m x + b
for example for day 15 and 16
1939.2 = m (15) + b
1943.9 = m (16) + b
 subtract
 4.7 = 1 m
so
m = 4.7  slope That is the "rate of change" for part b
back for b value
1939.2 = (4.7)(15) + b
b = 1868.7
so for the first two points the line is
price = 4.7*day + 1868.7
for the day 22
price = 4.7*22 + 1869.7
= 1973.1
The actual price on day 22 was 1909.9
There is no reason any combination of the prices of the previous week should predict the price on Monday. It happened that the price was going up fast between Monday and Tuesday. All we just did was assume that it continued to go up like that for a week, which it did not do. 
thanks