What is the equation of the line? picture attatched

y = -7x - 3

Step-by-step explanation:

The equation of the given line is

y = -7x + 2 and it contains the points (-5,32)

For two lines are parallel, their slopes must be equal.

Recall, the equation of a slope intercept is y = mx + c

Where m = slope

c = intercept

Comparing the equation given,

y = -7x + 2 with the equation if a straight line, y = mx + c,

The slope, m = -7

To find the equation that contains the points (-5,32), we will make use of the slope intercept equation again,

y = mx + c

Since the lines are parallel, the

slope = -7.

x= -5

y = 32

Using the slope intercept equation,

32 = -7 × -5 + c

32 = 35 + c

c = 32-35= -3

The equation is

y = -7x - 3

my guess would be b and d, but i didn’t actually get out the pen and paper. lol

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