Consider the graph shown.

what is the slope of the graph?
write an equation for the line.

i will mark you brainlest

The equation of line is .

Step-by-step explanation:

If a line passes through two points and , then the slope of the line is

From the given graph it is clear that the line is passes through the points (0,1) and (4,4).

The

The slope intercept form of a line is

where, m is slope and b is y-intercept

The slope of the line is and y-intercept is 1, so the equation of line is

Therefore, the equation of line is .

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