Which of the following represents a proportional relationship?(1 point)

Question

Responses

Image with alt text: An illustration shows a coordinate plane with the horizontal axis and vertical axis labeled x and y, but the unit increments are not marked. The origin is marked as 0. An upward diagonal line starting at the origin is plotted on the graph. The unmarked coordinates of the plotted line are left parenthesis 0 comma 0 right parenthesis, and left parenthesis 3 comma 9 right parenthesis. The line has an arrow at the end.

x y
−3 1
−2 2
−1 3

Answer 1

To determine if a relationship is proportional, we need to check if the ratio of \( y \) to \( x \) is constant.

Given the data points:

• For \( x = -3 \), \( y = 1 \): The ratio is \( \frac{1}{-3} = -\frac{1}{3} \)
• For \( x = -2 \), \( y = 2 \): The ratio is \( \frac{2}{-2} = -1 \)
• For \( x = -1 \), \( y = 3 \): The ratio is \( \frac{3}{-1} = -3 \)

Since the ratios are not constant, the given relationship is not proportional.

Now, considering the coordinate points provided in the image (assuming it depicts an upward diagonal line through the origin):

1. The line passes through the origin \( (0, 0) \).
2. Another point is \( (3, 9) \).

To check for proportionality:

The ratio of \( y \) to \( x \) at the point \( (3, 9) \) is: \[ \frac{9}{3} = 3 \]

Since the line goes through the origin and the ratio is constant, this represents a proportional relationship.

Therefore, the only proportional relationship is the one depicted in the image, where the line passes through the origin.