Final answer:
The derivative of the function y = 9 + 3x with respect to x, which is denoted as d y/d x, is the slope of the line, which is 3. Since the derivative of a constant is 0 and the derivative of 3x with respect to x is 3, the calculation is straightforward.
Step-by-step explanation:
The question asks for finding the derivative of the function y = 9 + 3x with respect to x, denoted as d y/d x. This function represents a straight line where the y-intercept is 9, and the slope (m) is 3, which corresponds to the coefficient of x in the equation. The derivative of a straight line is simply its slope, since the rate of change of y with respect to x is constant along the entire line.
To find d y/d x, you differentiate both sides of the equation with respect to x. Since the derivative of a constant is 0 and the derivative of 3x with respect to x is 3, the process looks like this:
- Start with the function y = 9 + 3x.
- Differentiate y with respect to x, leading to d y/d x.
- Since the derivative of a constant (9) is 0, it disappears in the derivative.
- The derivative of 3x with respect to x is 3.
- Therefore, d y/d x for the given function is 3.