Calculate the average rate of change over the interval from x=1 to x=3

The average rate of change over the given interval is 12

Step-by-step explanation:

Here, we want to calculate the average rate of change over the given interval

Mathematically, we can calculate the average rate of change using the formula below;

f(b) - f(a)/b-a

The f values are same as the y values

Thus, we have it that;

a = 1 and b = 3

f(a) = -5 and f(b) = 19

The average rate of change is thus;

(19-(-5))/(3-1) = 24/2 = 12

The point-slope form of the equation with slope of one half and passing through point (6, -3) is: y +3 = one half(x - 6).

Step-by-step explanation:

The general formula for point-slope form is (y-y,) = m(x-x,) where m= slope and (x, , y,) represents a point on the line.  In order to find the equation the represents the line given, you simply need to fill in the variables 'm', 'x,' and 'y,' with the values given.  In this case (6, -3) means x, = 6 and y, = -3 and slope is one half.  (y - (-3)) = one half (x - 6) or simplified (y + 3) = one half (x -6).