​A proportional relationship is based on equivalent ratios

Or multiplicative relationships only.... no adding or subtracting or exponent or square root steps... just multipliccaiton.

Ask yourself...

If I start with x and end with y, what did I multiply x by?

Does it look like I need to divide to get from x to y? If so, what would that look like as multiplication?

What if I work backwards and do the y values divided by the x values?

Characteristics of Proportional Graphs.

• They are always graphed as a straight line.

• They start at or cross through the origin

  • Graphs of proportional relationships must contain (0,0) since any number times zero is zero​

Characteristics of Non-Proportional Graphs.

• A graph is non-proportional if it meets ANY of these:

  • It isn't a straight line (bottom picture)

  • It doesn't go through the origin (top picture)

How to tell if a Graph is Proportional?

Constant of Proportionality in a Table​

• Represented by k

• The way to find k, the constant of proportionality, is to do y/x

• It is the same unit rate or "how much per one" you calculated in 6th grade 

• It is the multiplicative rule or relationship from one unit to the next.

• THE TABLE MUST HAVE A CONSTANT OF PROPORTIONALITY TO BE PROPORTIONAL.​

​y/x

1/2 = 0.5

2/4 = 0.5

3/6 = 0.5

4/8 = 0.5

5/10 =0.5

The table is proportional​

​Constant of Proportionality from a table?

Must Divide: ** y ➗​ x **

Proportional Equations

​3 is the C.O.P.

Constant of Proportionality 

​To write an equation, find the multiplicative rule...

Some text here about the topic of discussion

​​x = number of items

y = cost​

​

y = kx and k = 5​

y = 5x

Is the equation​​

​k = y/x

​ = 5/1 = 5

​ = 25/5 = 5

​ = 50/10 = 5

​ = 250/50 = 5

k = 5​

​x

y​

Find the constant of Proportionality from a graph

How do we find the COP from a graph?