Question

card sort
sort the cards into two groups based on whether they represent proportional relationships.
proportional relationship
not a proportional relationship
a
c
e
b
d

Explanation:

Step1: Recall the definition of proportional relationship

A proportional relationship has the form \(y = kx\) (where \(k\) is a constant) and passes through the origin \((0,0)\). For a table of values, \(\frac{y}{x}\) should be constant for non - zero \(x\) values.

Step2: Analyze Card A

For Card A:
When \(x = 4,y = 5\), \(\frac{y}{x}=\frac{5}{4}=1.25\)
When \(x = 8,y = 10\), \(\frac{y}{x}=\frac{10}{8}=1.25\)
When \(x = 12,y = 15\), \(\frac{y}{x}=\frac{15}{12}=1.25\)
And \((0,0)\) is present. So it is a proportional relationship.

Step3: Analyze Card B

For Card B:
When \(x = 2,y = 4\), \(\frac{y}{x}=\frac{4}{2}=2\)
When \(x = 4,y = 16\), \(\frac{y}{x}=\frac{16}{4}=4\)
The ratio \(\frac{y}{x}\) is not constant. So it is not a proportional relationship.

Step4: Analyze Card C

For Card C:
Since when \(x = 0,y = 2\) (does not pass through \((0,0)\)). So it is not a proportional relationship.

Step5: Analyze Card D

For Card D:
When \(x = 1,y = 10\), \(\frac{y}{x}=10\)
When \(x = 2,y = 8\), \(\frac{y}{x}=4\)
The ratio \(\frac{y}{x}\) is not constant. So it is not a proportional relationship.

Step6: Analyze Card E

For Card E:
When \(x = 2,y = 5\), \(\frac{y}{x}=\frac{5}{2}=2.5\)
When \(x = 8,y = 20\), \(\frac{y}{x}=\frac{20}{8}=2.5\)
When \(x = 1,y = 2.5\), \(\frac{y}{x}=2.5\)
When \(x = 20,y = 50\), \(\frac{y}{x}=\frac{50}{20}=2.5\)
So it is a proportional relationship.

Answer:

• Proportional Relationship: A, E
• Not a Proportional Relationship: B, C, D