Find the slope of the line passing through the points at (a, a+3) and (4a, a-5).

2) Together, two printers can print 7500 lines if the first printer prints for 2 minutes and the second prints for 1 minute. If the first printer prints for 1 minute and the second prints for 2 minutes, they can print 9000 lines together. Find the number of lines per minute that each printer prints.

1) To find the slope of the line passing through the points (a, a+3) and (4a, a-5), we can use the formula for slope:

slope = (y2 - y1) / (x2 - x1)

Here, (x1, y1) = (a, a+3) and (x2, y2) = (4a, a-5).

Plugging these values into the formula, we get:

slope = ((a-5) - (a+3)) / (4a - a)

Simplifying the numerator, we have:

slope = (a - 5 - a - 3) / (4a - a)
= (-8) / (3a)

Therefore, the slope of the line passing through the given points is -8 / (3a).

2) Let's assume that the first printer prints at a rate of x lines per minute, and the second printer prints at a rate of y lines per minute.

We can set up two equations based on the given information:

2x + y = 7500 -- equation (1)
x + 2y = 9000 -- equation (2)

To solve these equations, we can use the method of substitution:

From equation (2), we can isolate x and express it in terms of y:
x = 9000 - 2y

Substituting x into equation (1), we get:
2(9000 - 2y) + y = 7500
18000 - 4y + y = 7500
-3y = 7500 - 18000
-3y = -10500
y = -10500 / -3
y = 3500

Substituting the value of y back into equation (2), we can find the value of x:
x + 2(3500) = 9000
x + 7000 = 9000
x = 9000 - 7000
x = 2000

Therefore, the first printer prints at a rate of 2000 lines per minute, and the second printer prints at a rate of 3500 lines per minute.

1) Slope = (y2 -y1)/(x2 - x1) = -8/(3a)

The answer will depend upon a.

2. Lines printed = S1*t1 + S2*t2
S1 is the speed of printer 1 and t1 is the printing time of printer 1, etc.
7500 = 2 S1 + S2
9000 = S1 + 2 S2
Continue the solution