Rates and Proportional Relationships

proportional relationships

I can: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways

​Unit Rate

​Unit Rate is the rate of change for one unit. It is also known as the rate of change. With unit rate it must go up at a constant rate so the same amount every time.

​When trying to find the unit rate you want to make sure the change is the same every time

​Unit Rate equation

​Unit rate can be described by ​y=mx

​y is the dependent variable (or y value shown in a chart or graph)

m is the unit rate or rate of change

x is the independent variable (or x value shown in a chart or graph)

​With a little bit of work the equation can be used m=y/x

​How can we see unit rate

​Tables- In a table you have an x and y coloum. It shows the relationship between x and y. We want to find if the relationship is proportional. If it is then x and y will go will go up at the same rate or have the same unit rate

​X Y

​1......................3

​2...............6

​3...............9

​4.............12

​Examples of unit rate tables

​What tables are proportional?

​x......y

​1...............2

​2.............4

​3............6

​4............8

​​x......y

​1..............7

​2.............14

​3............21

​4............28

​​​x......y

​1..............6

​2.............12

​3............24

​4............48

​​​x......y

​1..............4

​3.............12

​4............16

​7............28

​How to see unit rate

​Graphs- A graph also shows the relationship between x and y. With graphs you need 2 points. Find the distance between them using the eq. y₂-y₁/x₂-x₁

​Since it is a stright line it is proportional

Multiple Choice

Find the slope of the line

• 3/2

• 2/3

• 4/7

• 3/5

​Word problems!

The steepness of a wheelchair ramp measures 6 inches in height for every 1 foot of horizontal distance. • Complete the table of values for the first 8 feet of a ramp. • Write an equation that can be used to represent the height (y) of the ramp in relation to the horizontal distance (x). • Graph the equation that represents the steepness of the wheelchair ramp

Open Ended

What did the lesson help you understand? And what are you still confused on?