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自变量c扩大10倍，因变量F会产生怎样的倍数关系

To analyze the relationship between the independent variable \( c \) and the dependent variable \( F \) shown in the uploaded image, we first need to understand the given equation:

\[ F = kc \]

where \( k \) is a constant of proportionality.

If the independent variable \( c \) is increased by a factor of 10, we substitute \( 10c \) for \( c \) in the equation:

\[ F = k(10c) = 10(kc) \]

Thus, the dependent variable \( F \) will also increase by a factor of 10.

So, if the independent variable \( c \) is multiplied by 10, the dependent variable \( F \) will also be multiplied by 10.

Would you like more details or have any other questions? Here are some more questions you might consider:

1. What is the significance of the constant \( k \) in the equation \( F = kc \)?
2. How would the relationship change if \( F \) were a nonlinear function of \( c \)?
3. Can we apply this multiplication rule to any linear function? Why or why not?
4. How does changing the independent variable affect the graph of the function \( F = kc \)?
5. What are some real-life examples of linear relationships similar to \( F = kc \)?

**Tip:** When dealing with linear relationships, any change to the independent variable will proportionally affect the dependent variable by the same factor.

Explore the linear relationship between variables in the equation F = kc. Understand how increasing the independent variable c by a factor of 10 impacts the dependent variable F. Gain insights into proportionality and linear functions. Suitable for students in Grades 9-12.

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