Direct Proportion When a quantity gets larger or smaller, we say that it changes. Sometimes a change in one quantity causes a change in another quantity. If these changes are related through equal factors, then the quantities are said to be in direct proportion or (directly proportional).

Direct Proportion Example of direct proportions abound in physics. For example, Newton's second law of motion states that the acceleration of an object is in direct proportion to the force on the object. So, if you triple the force on an object, then the acceleration of that object will also triple.

Example 2, suppose that you are buying cans of soup at the store Example 2, suppose that you are buying cans of soup at the store. Let us imagine that they cost $0.50 each. Case #1: Suppose that you buy 4 cans. You would pay $2.00. Case #2: Suppose that you buy 8 cans. You would pay $4.00. So, changing the number of cans that you buy will change the amount of money that you pay. Both the number of cans and the cost changed by the same factor, 2 – which is directly proportional.

Real World Problem In football, the number of points scored by field goals is a function of the number of field goals kicked. Make a function table showing the input (x) – field goals and the output (y) - # of points scored. Then graph it. How many field goals would be needed to score 21 points? 7 field goals

Real World Problem Wages are a function of the number of hours you work. If Billy Bob works X hours and gets paid $5.25 per hour, how much money does Billy make in 6 hours? Set up a function table. $31.50

Complete This Table n n - 3 5 10 21 32 2 7 18 29

Complete This Table x x + 6 5 10 21 32 11 16 27 38

What’s my rule? x y 2 1 4 6 3 10 5 X 2

What’s my rule? x y 1 6 2 15 3 24 4 33 8 69 9x-3

Graphing Functions

You should be able to: 1. Determine an algebraic expression for a situation. 2. Create a function table 3. Plot points on a coordinate plane

Step 1: To graph a function, use a function table to determine your coordinate points. (1, 2) (2, 4) (3, 6) (4, 8) X Y 1 2 4 3 6 8

Step 2: Plot the points on a coordinate plane. 1 4 3 2 8 7 6 5 10 9 (1, 2) (2, 4) (3, 6) (4, 8)

Step 3: Connect the dots if appropriate. Begin at the origin. 1 4 3 2 8 7 6 5 10 9 (1, 2) (2, 4) (3, 6) (4, 8)

Step 4: Write the function using the standard notation y = kx (also slope m) k is known as the constant of proportionality 1 4 3 2 8 7 6 5 10 9 HUH?

Constant of Proportionality- having the same or constant ratio In other words, the output increases or decreases by the same multiple each time. Y = 2X 2 is the constant

Step 5: Describe the characteristics of the graph 1 4 3 2 8 7 6 5 10 9 Is it increasing? Decreasing? Staying the same?

Step 6: Extend the graph to find other values of the function. 1 4 3 2 8 7 6 5 10 9 What would be the value if x=11?

Get out a sheet of paper. On the front, let’s make a t-chart (table) for our first student example. 1. Student #1 will see how many chairs he/she can hold at one time. 2. Complete the table for 2 students, 3 students, and 4 students and write a rule.

Below your first table, let’s make a t-chart (table) for our second student example. 1. Student #2 will see how many chairs he/she can hold at one time. 2. Complete the table for 2 students, 3 students, and 4 students and write a rule.

The number of chairs DEPENDS on which student is lifting them up The number of chairs DEPENDS on which student is lifting them up. Therefore, the number of chairs is called the DEPENDENT VARIABLE. The student is the INDEPENDENT VARIABLE because that value is not dependent upon anything else.

Another way to think about dependent and independent variables… Another way to think about dependent and independent variables…. INPUT values are the INDEPENDENT variables! Input (x) Output (y) Independent Dependent

Using the values from the table (t-chart), graph the points for Student #1 in one color and graph the points for Student #2 in another color.

Think about this one…. A can of Sprite has 140 calories Think about this one…. A can of Sprite has 140 calories. Make a table to show the calories in 3 cans, 7 cans, and 10 cans. Which value is the DEPENDENT variable and which is the INDEPENDENT variable?

Think about this one…. 3 children can play at Monkey Joe’s for $21 Think about this one…. 3 children can play at Monkey Joe’s for $21. Make a table to show the price of 1 child, 6 children, and 9 children. Which value is the DEPENDENT variable and which is the INDEPENDENT variable?

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