The grain is pumped out of a full-grain silo into a barge at a rate of 9 cubic meters per minute. The silo holds 2000 cubic meters of grain. Let y be the cubic meters remaining in the silo after x minutes. Write an equation in slope-intercept form that models the amount of grain in the silo. How would I solve this?

Explanation:

x = number of minutes

y = amount of grain left over, in cubic meters

We can abbreviate "cubic meters" into "m^3" without quotes of course.

The silo holds 2000 m^3 of grain. This is the initial value, so it is the y intercept. This means b = 2000. If the silo wasn't completely full, then we'd have to use a different initial value.

The slope is -9 because the amount of grain decreases by 9 cubic meters per minute. We can think of it like

slope = rise/run = (change in y)/(change in x)

slope = (change in grain)/(change in time)

Saying slope = -9/1 means the change in grain is -9 m^3 and the change in time is 1 minute.

Because the slope is -9, we say that m = -9

Therefore, we go from y = mx+b to y = -9x+2000

Note how plugging x = 0 into the equation leads to

y = -9x+2000

y = -9*0+2000

y = 0 + 2000

y = 2000

Showing that after 0 minutes, aka at the start, we have 2000 m^3 of grain.

Then at the x = 1 minute mark, we have...

y = -9x+2000

y = -9*1+2000

y = -9+2000

y = 1991

Showing that the silo lost 9 m^3 of grain since 2000-1991 = 9.

The graph y = -9x+2000 is a straight line that goes through the two points (0,2000) and (1,1991).