Answer
average rate of change $6$.
$y=6x-1$
Work Step by Step
Step 1. Given $f(x)=x^2+3x+1$, we have $f(1)=1^2+3+1=5$, $f(2)=2^2+3(2)+1=11$,
Step 2. We can find the average rate of change from 1 to 2: $R=\frac{f(2)-f(1)}{2-1}=6$.
Step 3. The slope of the secant line is same as the the average rate of change $m=6$.
Step 4. Use point $(1,5)$, we have $y-5=6(x-1)$ or $y=6x-1$
