graphing and functions one of my problem says that the average slope formula is: $\dfrac{f(x_2)-f(x_1)}{x_2-x_1}$
It tells us the average slope over the interval from $x_1$ to $x_2$
Then it says to take the average slope of the function $x^2+3x+1$ over one unit intervals from $0$ to $10$. 

can i use a particular function function to solve this problem?
As André said, what they want is the 10 numbers
$$\frac{f(1)-f(0)}{1-0}, \frac{f(2)-f(1)}{2-1}, \ldots, \frac{f(10)-f(9)}{10-9}$$
-- that is, with $x_1$ increasing from $0$ to $9$ while $x_2$ increases from $1$ to $10$. Then plot them against the $x_1$ values for each of them, and look for a pattern.
$f(x)=x^2+3x+1, x_1=0, x_2=10$
so the average slope on the interval [0,10] is $\frac{f(10)-f(0)}{10-0}=\frac{131-1}{10}=13$. 

If you want the average slope over all 1 unit intervals $[a, a+1]$ for $0\le a\le 9$ then this is the symbolic expression $\frac{f(a+1)-f(a)}{a+1-a}$ which simplifies to $2a+4$.

For example with $a=4.5$ we also get average slope of 13, but for $a=9$ we get average slope of 22.