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Algebraic Rules

Algebraic Rules. Please view this tutorial and answer the follow-up questions on loose leaf to turn in to your teacher. Algebraic Rules Basics. Algebraic rules are equations that use variables to model different situations.

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Algebraic Rules

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  1. Algebraic Rules Please view this tutorial and answer the follow-up questions on loose leaf to turn in to your teacher.

  2. Algebraic Rules Basics • Algebraic rules are equations that use variables to model different situations. • There will be two variables in these equations; one representing the x information and the other representing the y information

  3. How to Make an Algebraic Rule First you need to figure out what the variables are in your situation. Then you need to find letters to represent these variables.

  4. How to Make an Algebraic Rule Let’s take a look at this example problem. A bus driver is driving a school bus. He leaves the bus depot and goes on his route. He picks up four students at each stop. Write a rule to determine the number of people on the bus after each number of stops.

  5. How to Make an Algebraic Rule What are the two variables in this problem? The variables are the number of people on the bus and the number of stops. A bus driver is driving a school bus. He leaves the bus depot and goes on his route. He picks up four students at each stop. Write a rule to determine the number of people on the bus after each number of stops. number of people number of stops

  6. How to Make an Algebraic Rule Now that we know what the variables are, we can assign letters to represent them. P = Number of people on the bus N = Number of stops Now think about the important information in your problem.

  7. How to Make an Algebraic Rule The bus driver starts as the only one on the bus so our starting value is 1. How many people are initially on the bus? A bus driver is driving a school bus. He leaves the bus depot and goes on his route. He picks up four students at each stop. Write a rule to determine the number of people on the bus after each number of stops. A bus driver is driving a school bus.

  8. How to Make an Algebraic Rule How does the number of people on the bus change at each stop? At each stop the number of people on the bus increases by 4. A bus driver is driving a school bus. He leaves the bus depot and goes on his route. He picks up four students at each stop. Write a rule to determine the number of people on the bus after each number of stops. picks up four students

  9. How to Make an Algebraic Rule So, here is what we know: What can we control in this situation? The number of stops or the number of people on the bus? P = Number of people on the bus N = Number of stops Starting Value: 1 Change: Increase by 4 students per stop

  10. How to Make an Algebraic Rule We can control the number of stops so that means N is our independent variable. We can use this value to find P, the number of people on the bus. So, here is what we know: P = Number of people on the bus N = Number of stops Starting Value: 1 Change: Increase by 4 students per stop

  11. How to Make an Algebraic Rule Your rule will start with your dependent variable then an equal sign. So, here is what we know: P = Number of people on the bus N = Number of stops P = Starting Value: 1 Change: Increase by 4 students per stop

  12. How to Make an Algebraic Rule Then you’ll add your starting point. So, here is what we know: P = Number of people on the bus N = Number of stops P = 1 Starting Value: 1 Change: Increase by 4 students per stop

  13. How to Make an Algebraic Rule Finally, you’ll add an expression for how your values are changing. So, here is what we know: P = Number of people on the bus N = Number of stops P = 1 + 4N Starting Value: 1 Change: Increase by 4 students per stop

  14. How to Make an Algebraic Rule You’re increasing the number of people by 4 per stop so you multiply 4 by N. So, here is what we know: P = Number of people on the bus N = Number of stops P = 1 + 4N Starting Value: 1 Change: Increase by 4 students per stop

  15. Rules, Tables, and Graphs Now that we have our rule, we can use it to make tables and graphs. Hit Y= then enter your equation. You’ll need to replace your independent variable, N, with X.

  16. Rules, Tables, and Graphs Now that we have our rule, we can use it to make tables and graphs. Your rule should look like this.

  17. Rules, Tables, and Graphs Once the rule is in Y=, we can easily make tables and graphs. To make a table, click the 2nd Key then WINDOW

  18. Rules, Tables, and Graphs You’ll come to this screen. TblStart will be the x value that your table will start at. ΔTbl will be the value that the x column will count by in your table.

  19. Rules, Tables, and Graphs Next, you’ll need to make the table. Hit 2nd then GRAPH.

  20. Rules, Tables, and Graphs Your table will come up on your screen. Now you can scroll down the table to find exact values for x and y.

  21. Rules, Tables, and Graphs Sometimes you’ll be looking for a specific value. If you’re looking for a specific x value, go back to TBLSET (2nd WINDOW) then change your TblStart to the value you are looking for. Let’s say you want to know how many people will be on the bus after 15 stops.

  22. Rules, Tables, and Graphs Sometimes you’ll be looking for a specific value. Go to 2nd WINDOW then change your TblStart to 15. Then go to 2nd GRAPH to look for your answer in the table.

  23. Rules, Tables, and Graphs Sometimes you’ll be looking for a specific value. When X = 15, Y = 61 so after 15 stops there will be 61 people on the bus.

  24. Rules, Tables, and Graphs Sometimes you’ll be looking for a specific value. Suppose you want to know how many stops it will take until there are 25 people on the bus. If you’re looking for a specific y value, you’ll need to scroll down in the y column of your table to find that value.

  25. Rules, Tables, and Graphs Sometimes you’ll be looking for a specific value. Scroll down in your y column until you see the number 25.

  26. Rules, Tables, and Graphs Sometimes you’ll be looking for a specific value. When y = 25, x = 6 so there will be 25 people on the bus after 6 stops.

  27. Rules, Tables, and Graphs Sometimes you’ll be looking for a specific value. If you can’t find the value you are looking for, find the closest value to it then change your ΔTbl to a smaller number.

  28. Rules, Tables, and Graphs Your x values will now count by .1 since you changed ΔTbl.

  29. Follow-Up Questions Answer the following questions on loose leaf and hand them in to your teacher.

  30. On a plane, there are eighty-three rows that hold six people each. When the plane lands, the flight attendants dismiss passengers in groups of 18 people. Assuming the flight was filled to capacity (meaning it was sold out), how many passengers would there be on the plane. Write an algebraic rule to find the amount of passengers that still need to get off the plane in terms of groups. Using your calculator, make a table for the number of passengers left on the plane for the first ten groups. (Start at 0) How many people still need to get off the plane after 18 groups are dismissed? How many groups do they have to dismiss in order for everyone to get off the plane. Explain how you got your answer.

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