Problem 1
x = duration in seconds
y = number of pages
The 1st printer has the equation y = x-30 where x > 30.
For example, if x = 31 seconds have elapsed, then y = x-30 = 31-30 = 1 page has been printed. It turns out that the x-intercept will tell us when that 1st page will be printed. The x-intercept for y = x-30 is 30, which means the 31st second is when the first page is printed.
Now let's find the equation for the 2nd printer. The three points on this line are:
Pick two of those points to determine the slope. I'll select the first two points.
m = (y2 - y1)/(x2 - x1)
m = (32-16)/(60-40)
m = 16/20
m = 0.8
Now use point-slope form to do the following steps:
y - y1 = m(x - x1)
y - 16 = 0.8(x - 40)
y - 16 = 0.8x - 32
y = 0.8x - 32 + 16
y = 0.8x - 16
If you were to plug in y = 0 and solve for x, then,
y = 0.8x - 16
0 = 0.8x - 16
16 = 0.8x
0.8x = 16
x = 16/0.8
x = 20
The warm-up time for the 2nd printer is 20 seconds, which is less than the warm-up time for the 1st printer (30 seconds).
Answer: The first printer.
========================================================
Problem 2
Plug x = 100 into the 1st equation
y = x-30
y = 100-30
y = 70
The 1st printer can print out 70 pages in 100 seconds.
Repeat for the 2nd equation.
y = 0.8x-16
y = 0.8*100-16
y = 80-16
y = 64
The 2nd printer can print 64 pages in 100 seconds.
So even though the 1st printer needs a longer warm-up time, its rate or speed is faster than the 2nd printer to be able to print more pages.
Answer: The first printer.