Question

describe how the value of f(4) - f(1)
---------
4-1

is related to the graph of f(x)=6x-5

Answer 1

f(4) = 6(4) - 5 = 19
f(1) = 6(1) - 5 = 1

Hence, f(4) - f(1) = 19 - 1 = 18.

Answer 2

my book says the awnser is" its the slope of the line segment that joins the 2 points (1,1) and (4,19)

Answer 3

{ f(4) - f(1) } / (4 - 1) is the slope of the graph.
Slope = m = (y2 - y1) / (x2 - x1) for the points (x1, y1) and (x2, y2)
where x1=1, y1=f(1); x2=4, y2=f(4)

Answer 4

{ f(4) - f(1) } / (4 - 1) is the slope of the graph.

Slope = m = (y2 - y1) / (x2 - x1) for the points (x1, y1) and (x2, y2)

where x1 =1, y1 = f(1) = (6 - 5) = 1; x2 = 4, y2 = f(4) = (24 -5) = 19

So the two points are: (1, 1) and (4, 19)

and the formula { f(4) - f(1) } / (4 - 1) is the slope of the line joining the two points (1, 1) and (4, 19)