review problems\n3. select all the pieces of information that would tell you x and y have a proportional…

review problems\n3. 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.\n□ y = 3x\n□ the turtle walks in a circle around the rock.\n□ the turtle walks away from the rock at a constant rate.\n□ after 4 min., the turtle has walked 12 ft. away from the rock.\n□ the turtle walks for a bit, and then stops for 1 min. before walking again.

review problems\n3. 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.\n□ y = 3x\n□ the turtle walks in a circle around the rock.\n□ the turtle walks away from the rock at a constant rate.\n□ after 4 min., the turtle has walked 12 ft. away from the rock.\n□ the turtle walks for a bit, and then stops for 1 min. before walking again.

Answer

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.