Write the point-slope form of the line that passes through (-8, 2) and is parallel to a line with a slope of -8. Include all of your work in your final answer. Type your answer in the box provided to submit your solution.

y - 2 = -8(x + 8)

Step-by-step explanation:

Parallel lines have equal slope

Therefore, the slope of the line that passes through (-8, 2) is equal to -8 which is also the slope of the line parallel to it.

The slope of a line is given by

m = (y - y1) / (x - x1)

m = -8

Point (-8, 2) corresponds to (x1, y1)

Therefore, x1 = -8; y1 = 2

In, m = (y - y1) / (x - x1), we substitute the known values

-8 = (y - 2) / (x - (-8))

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

Cross multiply

y - 2 = -8(x + 8)

The point-slope form of the equation of a line is written as

y - y1 = m(x - x1)

In comparison,

y - y1 = m(x - x1) is equivalent to

y - 2 = -8(x + 8)

Therefore, the point-slope form of the line that passes through (-8, 2) and is parallel to a line with a slope of -8 is

y - 2 = -8(x + 8)

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.