Solution:
The average rate of change is denoted by A.R.C = h(6) - h(5) / 6 - 5
h(5) = (5)2 - 8 ( 5) = 25 - 40 = -15
h(6) = ( 6)2 - 8(6) = 36 - 48 = -12 A.R.C = [-12 - ( -15)] / 1 = (-12 + 15) / 1 = 3 /1 = 3
To find The equation of the secant line is to find the slope containing the points (5, h(5)) and ( 6, h(6))
the values of h( 5) and h(6) are substituted and the points are ( 5, -15) and (6 , -12)
The slope of the secant line m = -12 -(-15) / 6-5 = -12+15 / 1 = 3/1 =3 so the slope of the secant line is also the average rate of change
the equation of the secant line can be found by the slope equation form , so to find the equation of the secant line all you need is the slope of the line and one point located on the line. Choose point (6,-12)
and so you can write 3 = [y - (-12)] / (x - 6) , 3 = (y+12) / (x-6) , cross multiply you get y+12 = 3( x-6) ,
y+12 = 3x - 18 , y = 3x -18 -12 = 3x -30 so equation of secant line is y = 3x -30
Check by using point ( 5,-15) instead 3 = [y -(-15)] / (x -5) , 3( x-5) = y + 15 , 3x -15 -15 = y , 3x -30 = y or
y =3x-30 same answer as above
