Write an equation in slope-intercept form of the line through point p(8,2) with slope 4

Hello!

Firstly, we need to know what the slope-intercept form is. Slope-intercept form is y = mx + b. In this equation, m is the slope and b is the y-intercept.

Our goal here is to find the y-intercept. To find b, we will substitute the slope and the given ordered pair into the slope-intercept equation and solve algebraically.

y = mx + b (substitute the slope and point P)

2 = 2(8) + b (multiply)

2 = 16 + b (subtract 16 from both sides)

b = -14

Therefore, the equation is y = 2x - 14.

answer: entity is prob the answer

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