Please can you hlep with this.

Lines can be used to approximate a wide variety of functions; often a function can be described using many lines.

If a stock price goes from $10 to $12 from January 1st to January 31, from $12 to $9 from February 1st to February 28th, and from $9 to $15 from March 1st to March 31th is the price change from $10 to $15 a straight line?

It is clear that in each of the three time intervals mentioned there was a complex daily variation of prices as in an electrocardiogram. But what would be a simplified solution for a first naive view of the situation?

Would a simple function hold up?

What is the simplest function to represent this situation?

Does your nave initial and simplified model allow you to predict the behavior of the stock in the next month?

How can I use three "pieces" of lines to describe the price movements from the beginning of January to the end of March?

Show the graph for the price movement.

I started doing it but got completly stuck.

This is what i did:

Let's first write these out in a better format so we can understand it.

Price

Jan 1- $10

Jan 31 - $12

Feb 1 - $12

Feb 28 - $9

March 1 - $9

March 31 - $15

Now let's put in all the months into the formula for slopes (y2 - y1) / (x2 - x1)

January

(12-10)/(31-1)

(2)/(30)

Simplified this would be:

1/15

February

(9-12)/(28-1)

(-3)/(27)

Simplified this would be:

-1/9

March

(15-9)/(31-1)

(6)/(30)

Simplified this would be:

1/5

Now lets get the lines for each of these.

Now lets take y = mx + b and put in the first coordinates of each month.

January

y = mx + b

10 = 1/15 + b

Take 1/15 from each side

b = 10-1/15

b=149/15

b = 9.93

y = (1/15)(x) + 9.93

y = x/15 + 9.93

February

y = mx + b

12 = -1/9 + b

Add -1/9 to each side

b = 12 + 1/9

b = 109/9

b = 12.11

y = (-1/9)(x) + 12.11

y = -x/9 + 12.11

March

y = mx + b

9 = 1/9 + b

Take away 1/9 to each side

b = 9 - 1/9

b = 80/9

b = 8.88

y = (1/9)(x) + 8.88

y = x/9 + 8.88