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:

• For \(y = 3x\), it is in the form \(y=kx\) (where \(k = 3\)), which is the equation of a proportional relationship (\(y\) varies directly with \(x\)).
• If the turtle walks in a circle around the rock, the distance \(y\) (radial distance) is constant (\(y=r\), radius of the circle) and not related proportionally to time \(x\) (since \(y\) does not change as \(x\) changes in a \(y = kx\) - like fashion).
• If the turtle walks away from the rock at a constant rate, the relationship is \(y=kx\) (where \(k\) is the constant rate, \(y\) is distance, \(x\) is time), which is a proportional relationship.
• Just knowing that after \(4\) min (\(x = 4\)), the turtle has walked \(12\) ft (\(y=12\)) is a single - data point. We don't know if \(y\) and \(x\) follow \(y = kx\) for all \(x\) values (e.g., if \(x = 1\), \(y\) could be \(12\) if it's a non - proportional start - up, or \(y = 3\) if \(y=3x\)).
• If the turtle stops for \(1\) min, the relationship between \(y\) (distance) and \(x\) (time) is not of the form \(y = kx\) (because the rate is not constant for all \(x\) values, there is a period where \(y\) does not change as \(x\) increases by \(1\) min).

Answer:

\(\square y = 3x\), \(\square\) The turtle walks away from the rock at a constant rate.