Take a real-life situation and create an equation or inequality that could be used for analysis, prediction, or decision making. Then, draw a graph to depict the variables in your situation Use your graph and what you know about linear inequalities to discuss the significance of your findings
This was my answer:
A good example for me of a straight line graph is to figure out your income for that specific pay period. I do this every week before I get paid. And now I am using it to my advantage to apply this activity to my math work. Every week before I get paid I calculate my hours times my rate of pay which would be a constant since I know I make $7.50 an hour. So then I can figure out the total pay I will receive. This may not work for everyone though; I have a set 40 hours a week. Some peoples hours worked may vary.
For the linear equation I would use my 4 year CD savings account as the example. I opened the account 1 year ago with a deposit of $1200. Since it is a CD account I cannot touch the money for 4 years until the required time is up (unless I close it before then, in which case I will be charged and early termination fee). The account has an interest rate of 0.09%, meaning so far I have made $108. Now I can use the known information to figure out how much money will be in the account after 4 years. The slope (which will be going up in a positive form) will represent how much money I have gained from interest each year.
To analyze and predict the amount of money in your 4-year CD savings account, you can create a linear equation. Let's represent the number of years since opening the account as "x," and the total amount of money in the account after 4 years as "y."
The initial amount deposited in the account was $1200, and the interest rate is 0.09%. Based on this, we can write the equation:
y = 1200 + 0.09x
Now, let's draw a graph to depict this situation. On the x-axis, we will represent the number of years (x) and on the y-axis, the total amount of money in the account after 4 years (y). We can plot some points to illustrate the relationship:
When x = 0 (account just opened), y = 1200 + 0.09(0) = 1200.
When x = 1 (1 year has passed), y = 1200 + 0.09(1) = 1209.
When x = 2 (2 years have passed), y = 1200 + 0.09(2) = 1218.
When x = 3 (3 years have passed), y = 1200 + 0.09(3) = 1227.
When x = 4 (4 years have passed), y = 1200 + 0.09(4) = 1236.
Now, let's plot these points on the graph and draw a straight line passing through them:
|
1236 | *
|
1227 | *
|
1218 | *
|
1209 | *
|
1200 | *
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0 1 2 3 4 x
The significance of this graph is that it shows the steady increase in the total amount of money in your CD savings account over the 4-year period. The slope of the line represents the interest gained each year, which in this case is 0.09 (or 9%).
By analyzing this graph, you can predict the future value of your savings account after any number of years within the 4-year period. You can also compare different interest rates or deposits to see how they would impact the growth of your savings over time.