Notes Constant rate of change as slope

Notes Constant rate of change as slope

Ratio and Rate Review

• A ratio compares two or more objects for instance apples to oranges or cats to dogs

• A rate compares a change between to or more objects such as miles per hour .

Constant Rate of change

The image to the left shows the number of transactions increasing by 3

Balance decreases by 30

This shows a constant rate of change of -10 for each transaction.

Fill in the Blank

When the number of transactions changed from 3 transactions to 6 transactions there was a change of how much in the balance?

Fill in the Blank

The example to the left shows a balance change of -30 dollars for every three transactions. What is the dollar change per one transaction? (Enter integer value as answer)

Proportional Relationships

Ratios are equal

Rate of change is constant

Linear Relationship

A relationship between two objects that have a constant rate of change is called linear. If we graph these points you will see they make a straight line.

We can see that the rate of change is equivalent. If the ratios are also equivalent then the relationship is proportional.

15/2=7.5 and 30/4=7.5 and 45/6=7.5

Fill in the Blank

If we divide each ratio we get the same number. What is the ratio?
 $\frac{Money\ earned}{time\ spent\ mowing}\$  

 $\left(Money\ earned\right)\ \div\ \left(time\ spent\ mowing\right)$   

Multiple Choice

If the rate of change is constant and the rates are equivalent the relationship is:

• Proportional

• Non proportional

Multiple Choice

Is the relationship proportional or non-proportional?

• Proportional

• Non-proportional

Multiple Choice

Is the following proportional or non-proportional?

• Proportional

• Non-Proportional

Why are graphs important?

• They show us rate of change

• They show us proportionality

Graphs and tables

The table shows a constant rate of change

This is also seen on the graph because the points make a straight line.

The relationship is not proportional because the ratios are not equivalent.  When the ratios are equivalent the line goes through the origin (0,0)

Multiple Choice

What are the main characteristics of a proportional relationship between two variables?

• They pass through the origin.
• They are linear and also pass through the origin.
• They are curved
• They have a negative relationship and pass through the origin.

Multiple Choice

Proportional or Non-Proportional?

• Proportional

• Non-Proportional

Multiple Choice

Proportional or Non-Proportional?

• Proportional

• Non-Proportional

Multiple Choice

Proportional or Non-Proportional?

• Proportional

• Non-Proportional

Multiple Choice

What is the rate of change for the following graph?

• 80
• 20
• 40
• 160

Multiple Choice

At what rate did the rain fall?

• 2 cm per hour
• ¹/₄ cm per hour
• ¹/₂ cm per hour
• 4 cm per hour

Multiple Choice

What is the constant of proportionality for this table?

• 1/9
• 9
• 8

Multiple Choice

Which company shows a greater rate of change?

• Water's Edge Rafts
• Ryan's Rafts