Write an equation of the line that passes through the given point and is parallel to the given line. (4, 3); y = –x + 5

Remember that the standard form of a line equation is y = mx + b.   Since you need a line that is parallel to y = 5x - 2, the first thing to do is use the same slope (m), which is 5 in this case.

The new line would look like this:  y = 5x + b.  I use "b" instead of -2, since we'll calculate a "b" for the new line by substituting the given point of (2, -1) into y = 5x + b.

 -1 = 5*(2) + b

 b = -11  

The parallel line that goes through (2,-1) is y = 5x - 11

The new line is the blue, on the right.  Note that it is parallel to the original (green) line and also intersects at  (2, -1).  (Each chart is is 0.5 unit).

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.