Question

review problems

1. select all the pieces of information that would tell you x and y have a proportional relationship. let y represent the distance in feet (ft.) between a rock and a turtles current position, and let x represent the time in minutes (min.) the turtle has been moving for.

□ y = 3x
□ the turtle walks in a circle around the rock.
□ the turtle walks away from the rock at a constant rate.
□ after 4 min., the turtle has walked 12 ft. away from the rock.
□ the turtle walks for a bit, and then stops for 1 min. before walking again.

Explanation:

Step1: Analyze \(y = 3x\)

The equation \(y=kx\) (where \(k = 3\) here) is the standard form of a proportional relationship.

Step2: Analyze "The turtle walks in a circle around the rock"

If the turtle walks in a circle around the rock, the distance \(y\) (from the rock) does not change proportionally with time \(x\). The relationship is not linear - proportional (since \(y\) is constant for non - zero \(x\) values in some intervals).

Step3: Analyze "The turtle walks away from the rock at a constant rate"

The formula for distance \(y=v\times x\) (where \(v\) is the constant rate). This is of the form \(y = kx\) (a proportional relationship).

Step4: Analyze "After 4 min, the turtle has walked 12 ft away from the rock"

We can find the rate \(k=\frac{y}{x}=\frac{12}{4}=3\). So the equation is \(y = 3x\), which is a proportional relationship.

Step5: Analyze "The turtle walks for a bit, and then stops for 1 min before walking again"

When the turtle stops, \(y\) does not change while \(x\) (time) is increasing. So the relationship is not proportional.

Answer:

\(y = 3x\), The turtle walks away from the rock at a constant rate, After 4 min., the turtle has walked 12 ft. away from the rock.