Aprinter is initially loaded with 500 sheets of paper, and a job is printed. the printer prints at a constant rate of speed. after 10 minutes, it has used 25% of the paper. which of the following equations models the number of sheets of paper, p, remaining in the machine m minutes after the machine started printing?

p = -12.5m + 500
where p is the number of papers and m is the number of minutes

Explanation:
The points we have will be in the form of (m,p) where m is the minutes and p is the number of papers.
Now:
At m=0, the printer had 500 papers. Therefore, the first point is (0,500)
At m=10, the printer had consumed 0.25 of the paper available. This means that the printer had 0.75*500 = 375. Therefore, the second point is (10,375)

The general form of the linear equation is:
y = mx + c
in our case, it will be:
p = sm + c
where:
p is the number of papers
s is the slope
m is the number of minutes
c is the y-intercept

1-getting the slope:
slope = (y2-y1) / (x2-x1) = (375-500) / (10-0) = -12.5
The equation now is:
p = -12.5m + c

2-getting the y-intercept:
The two given points belong to the line. This means that these two points satisfy the equation of the line. Therefore, to get the y-intercept, we will use any of these points to substitute in the equations and solve for the unknown c.
I will use the point (0,500) as follows:
p = -12.5m + c
500 = -12.5(0) + c
c = 500
Therefore, the equation now becomes:
p = -12.5m + 500

Hope this helps :)