A s A p P p pP p p p p P P PP PpPppPP P P P PpPPPpP

the answer is three , but let me try to help explain...

in a line the slope (M) as in y=mx + b

is a constant number ... rise over run for every unit in the x direction the y changes by that amount

in your graph what you have to do is locate where the red line crosses the grid in a "nice"  (at the corner of a box) notice that at the 2 for yards it exactly crosses at the 6 for feet...

that suggests that the "slope", "proportional constant" ,rise over run".

"gradient"  what ever the word you want to use is 6/2 which is 3

Step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt