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