What is an equation of the line, in point-slope form, that passes through the given point and has the given slope? point: (5,6); slope: 2/3

equation of line:

y = mx + b(1)

slope = m = 2/3

y-intercept = b = ?

putting the point (5,6) and slope(2/3) in equation(1)

6 = (2/3)(5) + b

6 = 10/3 + b

b = 6 - 10/3

b = (18 - 10)/3

b = 8/3

putting value of b and m in equation(1)

y = (2/3)x + 8/3

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