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. 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 - 35

102132

27

1829

Complete This Table

x x + 65

102132

11162738

What’s my rule?

x y

2 14 26 3

10 5

X2

What’s my rule?

x y

1 62 153 244 338 69

9x-3

You should be able to: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.

X Y

1 2

2 4

3 6

4 8

(1, 2) (2, 4) (3, 6) (4, 8)

Step 2: Plot the points on a coordinate plane.

1

43210

8765

109

2 3 4 5 6 7 8 9 10

(1, 2) (2, 4) (3, 6) (4, 8)

Step 3: Connect the dots if appropriate. Begin at the origin.

1

43210

8765

109

2 3 4 5 6 7 8 9 10

(1, 2) (2, 4) (3, 6) (4, 8)

Step 4: Write the function using the standard notation y = kx

1

43210

8765

109

2 3 4 5 6 7 8 9 10

k is known as the constant of proportionality

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

43210

8765

109

2 3 4 5 6 7 8 9 10

Is it increasing? Decreasing? Staying the same?

Step 6: Extend the graph to find other values of the function.

1

43210

8765

109

2 3 4 5 6 7 8 9 10

What would be the value if x=11?

The End