Which equation has a constant of proportionality equal to 
\[10\]?
Choose 1 answer:
Choose 1 answer:
(Choice A)   
 
\[y=\dfrac{2}{20}x\]
A
 
\[y=\dfrac{2}{20}x\]
(Choice B)   
 
\[y=\dfrac{30}{3}x\]
B
 
\[y=\dfrac{30}{3}x\]
(Choice C)   
 
\[y=\dfrac{12}{2}x\]
C
 
\[y=\dfrac{12}{2}x\]
(Choice D)   
 
\[y=\dfrac{5}{5}x\]
D
 
\[y=\dfrac{5}{5}x\]

To determine which equation has a constant of proportionality equal to 10, we need to identify the coefficient of \(x\) in each equation, as the general form for a direct variation is \(y = kx\), where \(k\) is the constant of proportionality.

Let's evaluate each choice:

1. **Choice A**:  
   \[ y = \frac{2}{20}x = \frac{1}{10}x \]  
   Constant of proportionality \(k = \frac{1}{10}\).

2. **Choice B**:  
   \[ y = \frac{30}{3}x = 10x \]  
   Constant of proportionality \(k = 10\).

3. **Choice C**:  
   \[ y = \frac{12}{2}x = 6x \]  
   Constant of proportionality \(k = 6\).

4. **Choice D**:  
   \[ y = \frac{5}{5}x = 1x \]  
   Constant of proportionality \(k = 1\).

The only equation with a constant of proportionality equal to 10 is **Choice B**:  
\[ y = \frac{30}{3}x \]

Would you like further details or explanations? Here are some related questions you might consider:

1. What does the constant of proportionality represent in a linear equation?
2. How do you convert a fraction into a decimal?
3. Can you explain how to identify constants of proportionality in other forms of equations?
4. What are some real-world applications of proportional relationships?
5. How does changing the constant of proportionality affect the graph of the equation?

**Tip**: Always check the coefficient of \(x\) in the equation to quickly determine the constant of proportionality.

Which equation has a constant of proportionality equal to 10?

Explore how to identify the constant of proportionality in various linear equations. This problem provides a step-by-step solution to find which equation has a constant of proportionality equal to 10. Suitable for students in Grades 6-8.

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