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
[tex]y = 3x[/tex]
Required
Determine which of the options answers the question
Recall that:
[tex]y = distance[/tex]
[tex]x = time[/tex]
Analyzing the options 1 after the other:
Option 1:
In this option, we have that:
[tex]y = 12[/tex]
[tex]x = 4[/tex]
Substitute these values of x and y in the given equation
[tex]y = 3x[/tex]
[tex]12 = 3 * 4[/tex]
[tex]12 = 12[/tex]
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
[tex]y = 3x[/tex]
Assume [tex]x = 5[/tex]
y would be
[tex]y = 3 * 5[/tex]
[tex]y = 15[/tex]
Assume [tex]x = 6[/tex]
y would be
[tex]y = 3 * 6[/tex]
[tex]y = 18[/tex]
For every values of x and corresponding y value, there exist a constant relationship because:
[tex]\frac{y}{x} = 3[/tex]
This implies that the rate at which the turtle moved is 3ft/s and this rate is constant.
