To determine which ordered pair [tex]\((x, y)\)[/tex], where [tex]\(x\)[/tex] represents the number of days that a library book is late and [tex]\(y\)[/tex] represents the total fee, is a viable solution, we need to verify the relationship given by the late fee charge of $0.30 per day.
Given the late fee rate:
[tex]\[ y = 0.30x \][/tex]
Let's check each ordered pair:
1. For [tex]\((-3, -0.90)\)[/tex]:
[tex]\[
y = 0.30 \times (-3)
\][/tex]
[tex]\[
y = -0.90
\][/tex]
This ordered pair satisfies the equation [tex]\(y = 0.30x\)[/tex]:
[tex]\[
-0.90 = 0.30 \times (-3)
\][/tex]
2. For [tex]\((-2.5, -0.75)\)[/tex]:
[tex]\[
y = 0.30 \times (-2.5)
\][/tex]
[tex]\[
y = -0.75
\][/tex]
This ordered pair satisfies the equation [tex]\(y = 0.30x\)[/tex]:
[tex]\[
-0.75 = 0.30 \times (-2.5)
\][/tex]
3. For [tex]\((4.5, 1.35)\)[/tex]:
[tex]\[
y = 0.30 \times 4.5
\][/tex]
[tex]\[
y = 1.35
\][/tex]
This ordered pair satisfies the equation [tex]\(y = 0.30x\)[/tex]:
[tex]\[
1.35 = 0.30 \times 4.5
\][/tex]
4. For [tex]\((8, 2.40)\)[/tex]:
[tex]\[
y = 0.30 \times 8
\][/tex]
[tex]\[
y = 2.40
\][/tex]
This ordered pair satisfies the equation [tex]\(y = 0.30x\)[/tex]:
[tex]\[
2.40 = 0.30 \times 8
\][/tex]
From the above checks, all the given ordered pairs satisfy the relationship [tex]\( y = 0.30x \)[/tex]. However, we need to determine which of these solutions is considered viable based on additional given conditions or context we might interpret:
Among the ordered pairs, [tex]\((-2.5, -0.75)\)[/tex] closely matches the typical scenario where both the days late and the fee align perfectly with a simple, familiar fraction.
Therefore, the viable solution in this context is:
[tex]\[
(-2.5, -0.75)
\][/tex]
