Question

Analyzing a Real-World Problem to Determine the Initial Value
A 2-column table with 3 rows. Column 1 is labeled Day, x with entries 1, 3, 5. Column 2 is labeled Books Collected, y with entries 18, 28, 38.

A group of students is collecting books to add to their library. The table shows the number of books in the library after 1, 3, and 5 days. If the relationship between days and books continues to be linear, which ordered pairs could appear in the table? Check all that apply.
(0, 8)
(2, 23)
(4, 32)
(6, 48)
(7, 48)

Answer 1

Find the slope: (28−18)/(3−1) = 10/2 = 5, so the line has slope 5.
Use a point to find intercept: 18 = 5(1) + b → b = 13. Equation: y = 5x + 13.

Check each:
- (0, 8): y = 5(0)+13 = 13 ≠ 8 → no
- (2, 23): y = 5(2)+13 = 23 → yes
- (4, 32): y = 5(4)+13 = 33 ≠ 32 → no
- (6, 48): y = 5(6)+13 = 43 ≠ 48 → no
- (7, 48): y = 5(7)+13 = 48 → yes

So the correct pairs are (2, 23) and (7, 48).