Consider the function p(x) = x^2 + 6x + 5.
what is the average rate of change from x=1 to x=5

The average rate of change is 12.

Step-by-step explanation:

Given

p(x)= x^2+6x+5

The average rate of change in the given interval a ≤ x ≤ b is given by the expression

Rate of change=  (p(b)-p(a))/(b-a)

Here p(b) is the value of function at point b and p(a) is the value of function point a.  

From the question,

a = 1  

and  

b = 5

So,

Rate of change=  (p(5)-p(1))/(5-1)

Now,  

p(5)= (5)^2+6(5)+5

p(5)=25+30+5

p(5)=60

And

p(1)= (1)^2+6(1)+5

p(1)=1+6+5

p(1)=12

Putting in the formula

Rate of change=  (60-12)/(5-1)

=  48/4

=12

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: