Question

Select all of the pieces of information that would tell you x and y have a proportional relationship. Let y represent the distance in meters between a rock and a turtle's current position and x represent the time in minutes the turtle has been moving.

Answer 1

Complete Question:

Select all of the pieces of information that would tell you x and y have a proportional relationship.

Let y represent the distance between a rock and a turtle's current position in meters and x represent the number of minutes the turtle has been moving. y=3x

1. After 4 minutes, the turtle has walked 12 feet away from the rock.

2. The turtle walks for a bit, then stops for a minute before walking again.

3. The turtle walks away from the rock at a constant rate.

Answer:

1. After 4 minutes, the turtle has walked 12 feet away from the rock.

3. The turtle walks away from the rock at a constant rate.

Step-by-step explanation:

Given

$y = 3x$

Required

Determine which of the options answers the question

Recall that:

$y = distance$

$x = time$

Analyzing the options 1 after the other:

Option 1:

In this option, we have that:

$y = 12$

$x = 4$

Substitute these values of x and y in the given equation

$y = 3x$

$12 = 3 * 4$

$12 = 12$

Because both sides of the equation are equal, this option shows a proportional relationship

Option 2:

The given equation cannot be used to ascertain the information given in this option.

Because for a every time (in minutes) traveled by the turtle, there's a corresponding distance moved.

Option 3:

Recall that

$y = 3x$

Assume $x = 5$

y would be

$y = 3 * 5$

$y = 15$

Assume $x = 6$

y would be

$y = 3 * 6$

$y = 18$

For every values of x and corresponding y value, there exist a constant relationship because:

$\frac{y}{x} = 3$

This implies that the rate at which the turtle moved is 3ft/s and this rate is constant.