State whether the statement is True or False:
If `y = 7x+1`, then the rate of change of demand (`x`) of a commodity with respect to it’s price (`y`) is `7`.

Answer

To determine whether the statement is true or false, we need to analyze the relationship between the variables \( x \) (demand) and \( y \) (price) given by the equation \( y = 7x + 1 \).

### Step-by-Step Solution:

1. **Understand the given equation**:
The equation provided is:
\[ y = 7x + 1 \]

2. **Rearrange the equation to express \( x \) in terms of \( y \)**:
To find the rate of change of demand \( x \) with respect to price \( y \), we need to express \( x \) in terms of \( y \):
\[ y - 1 = 7x \implies x = \frac{y - 1}{7} \]

3. **Differentiate \( x \) with respect to \( y \)**:
Now, we differentiate \( x \) with respect to \( y \):
\[ \frac{dx}{dy} = \frac{d}{dy}\left(\frac{y - 1}{7}\right) \]
Since \( \frac{1}{7} \) is a constant, we can differentiate:
\[ \frac{dx}{dy} = \frac{1}{7} \]

4. **Compare the result with the statement**:
The statement claims that the rate of change of demand \( x \) with respect to price \( y \) is \( 7 \). However, we found that:
\[ \frac{dx}{dy} = \frac{1}{7} \]
This is not equal to \( 7 \).

5. **Conclusion**:
Therefore, the statement is **False**.