Find the difference quotient $\frac{f(x+h)-f(x)}{h}$, where $h \neq 0$, for the function belo \[ f(x)=7 x-1 \] Simplify your answer as much as possible.

Step 1 ：Given the function \(f(x)=7x-1\), we are asked to find the difference quotient \(\frac{f(x+h)-f(x)}{h}\), where \(h \neq 0\).

Step 2 ：Substitute \(x+h\) and \(x\) into the function to get \(f(x+h)=7(x+h)-1\) and \(f(x)=7x-1\).

Step 3 ：Subtract the two results to get the numerator of the difference quotient: \(f(x+h)-f(x) = 7(x+h)-1 - (7x-1) = 7h\).

Step 4 ：The denominator of the difference quotient is simply \(h\).

Step 5 ：So the difference quotient is \(\frac{f(x+h)-f(x)}{h} = \frac{7h}{h} = 7\).

Step 6 ：This means that the average rate of change of the function over the interval \(h\) is 7, regardless of the value of \(h\) (as long as \(h \neq 0\).

Step 7 ：This makes sense because the function \(f(x)=7x-1\) is a linear function with a slope of 7, so its rate of change is constant.

Step 8 ：Final Answer: The simplified difference quotient for the function \(f(x)=7x-1\) is \(\boxed{7}\).