Find `dy/dx if y=x-9`

Answer

To find \( \frac{dy}{dx} \) for the equation \( y = x - 9 \), we will follow these steps:

### Step 1: Identify the function
We start with the equation given:
\[ y = x - 9 \]

### Step 2: Differentiate the function
To find \( \frac{dy}{dx} \), we need to differentiate \( y \) with respect to \( x \). The differentiation rules state:
- The derivative of \( x \) with respect to \( x \) is \( 1 \).
- The derivative of a constant (in this case, \(-9\)) is \( 0 \).

So, we differentiate:
\[ \frac{dy}{dx} = \frac{d}{dx}(x) - \frac{d}{dx}(9) \]

### Step 3: Apply the differentiation rules
Applying the differentiation rules:
\[ \frac{dy}{dx} = 1 - 0 \]

### Step 4: Simplify the result
Thus, we simplify the result:
\[ \frac{dy}{dx} = 1 \]

### Final Answer
The derivative \( \frac{dy}{dx} \) is:
\[ \frac{dy}{dx} = 1 \]

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