Question

analyzing a real - world problem to determine the initial value
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.
the table has columns: day, x and books collected, y. rows: when x = 1, y = 18; when x = 3, y = 28; when x = 5, y = 38.
options: (0, 8); (2, 23); (4, 32); (6, 48); (7, 48)

Explanation:

Step1: Find the slope

We have two points \((1, 18)\) and \((3, 28)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{28 - 18}{3 - 1}=\frac{10}{2}=5\).

Step2: Find the linear equation

Using the point - slope form \(y - y_1=m(x - x_1)\) with the point \((1, 18)\) and \(m = 5\).
\(y-18 = 5(x - 1)\)
\(y-18=5x-5\)
\(y=5x + 13\)

Step3: Check each ordered pair

• For \((0,8)\): Substitute \(x = 0\) into \(y = 5x+13\), we get \(y=5\times0 + 13=13

eq8\).

• For \((2,23)\): Substitute \(x = 2\) into \(y = 5x + 13\), \(y=5\times2+13=10 + 13=23\).
• For \((4,32)\): Substitute \(x = 4\) into \(y = 5x+13\), \(y=5\times4+13=20 + 13=33

eq32\).

• For \((6,48)\): Substitute \(x = 6\) into \(y = 5x + 13\), \(y=5\times6+13=30+13 = 43

eq48\).

• For \((7,48)\): Substitute \(x = 7\) into \(y = 5x+13\), \(y=5\times7+13=35 + 13=48\).

Answer:

The ordered pairs that could appear in the table are \((2,23)\) and \((7,48)\) (i.e., the checkboxes for \((2,23)\) and \((7,48)\) should be checked).