Question

line passing through which of the following pairs of coordinates represents a proportional relationship?
A.
(1.25, 2.25) and (2.5, 5)
B.
(1.25, 2.5) and (3.75, 7.5)
C.
(1.3, 3.3) and (2.3, 4.3)
D.
(2.5, 5) and (3, 5.5)

Answer 1

A proportional relationship between two coordinates means that the ratio of the \( y \)-value to the \( x \)-value is constant.

Let's check each pair:

**A.** \((1.25, 2.25)\) and \((2.5, 5)\)

For (1.25, 2.25):
\[
\frac{y}{x} = \frac{2.25}{1.25} = 1.8
\]

For (2.5, 5):
\[
\frac{y}{x} = \frac{5}{2.5} = 2
\]

Since \( 1.8 \neq 2 \), this does not represent a proportional relationship.

---

**B.** \((1.25, 2.5)\) and \((3.75, 7.5)\)

For (1.25, 2.5):
\[
\frac{y}{x} = \frac{2.5}{1.25} = 2
\]

For (3.75, 7.5):
\[
\frac{y}{x} = \frac{7.5}{3.75} = 2
\]

Since both ratios are equal to \( 2 \), this represents a proportional relationship.

---

**C.** \((1.3, 3.3)\) and \((2.3, 4.3)\)

For (1.3, 3.3):
\[
\frac{y}{x} = \frac{3.3}{1.3} \approx 2.54
\]

For (2.3, 4.3):
\[
\frac{y}{x} = \frac{4.3}{2.3} \approx 1.87
\]

Since \( 2.54 \neq 1.87 \), this does not represent a proportional relationship.

---

**D.** \((2.5, 5)\) and \((3, 5.5)\)

For (2.5, 5):
\[
\frac{y}{x} = \frac{5}{2.5} = 2
\]

For (3, 5.5):
\[
\frac{y}{x} = \frac{5.5}{3} \approx 1.83
\]

Since \( 2 \neq 1.83 \), this does not represent a proportional relationship.

---

The only pair that represents a proportional relationship is **B. (1.25, 2.5) and (3.75, 7.5)**.