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)

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)

The missing table is given below.

The correct options are option 2:(2,23) and 5:(7,48) The ordered pair (2,23),(7,48) will appear in the table.

What is linear equation?

The equation where highest degree of the variable used in the equation is 1 is called linear equation. Foe example ax+by+c=0

Here given the relationship between days and books is linear.

From the table, it clear that In day 1 the book collected is 18.

in day 3 book collected is 28.

x₁=1,y₁=18

x₂=3,y₂=28

The linear equation will be

(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)

⇒(y-18)/(x-1)=(28-18)/(3-1)

⇒(y-18)/(x-1)=10/2

⇒(y-18)/(x-1)=5

⇒y-18=5(x-1)

⇒y-18=5x-5

⇒y=5x-5+18

⇒y=5x+13

So the linear equation will be y=5x+13

By ckecking every option,

1. (0, 8)- y=5*0+13=13≠8 Option 1 is incorrect.

2. (2,23)- y=5*2+13=23 Option 2 is correct.

3. (4,32)- y=5*4+13=33≠32 Option 3 is incorrect.

4.(6,48)- y=5*6+13=43≠48 Option 4 is incorrect.

5. (7,48) y=5*7+13=48 Option 5 is correct.

Therefore the correct options are option 2 and 5 i.e. The ordered pair (2,23) , (7,48) will appear in the table.

Learn more about linear equation

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