First, let's write the ordered pairs using the numbers we are given. The first number, 281000, represents the weight of the box as one item is taken out of it. Thus, the ordered pair is (1,281000). We can write the rest of them in a similar manner.
(1,281000),(2,270000),(3,259000),(4,248000)
Let's now use the slope-intercept form of the equation to write the function.
y=mx+b
We can calculate the slope m by substituting two arbitrary points from above into the . Let's use (1,281000) and (2,270000).
m=x2−x1y2−y1
m=2−1270000−281000
m=-11000
Thus, the slope is -11000. Now we can find b by substituting the slope and a point, let's use (2,270000), into the equation.
y=mx+b
y=(-11000)x+b
270=-11(2)+b
b=292000
Now we can write the function.
y=-11x+292000
We know the weights of the box after taking out each item. Hence, if we calculate the differences between consecutive weights, we will know the weight of each item.
281000−270000270000−259000259000−248000=11000=11000=11000
The weight of each yearbook is 11000 ounces.
It is given that the weight of the box when full is 292000 ounces, and when it's empty is 17000 ounces. Therefore, by subtracting 17000 from 292000 we can calculate the weight of all of the items, not including the weight of the box.
292000−17000=275000 ounces
Now if we divide this weight by the weight of 1 book, we will know how many items were in the box.
11000272000=25 items
There were 25 items in the box.