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 turtle’s
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.

1. decide whether each table could represent a proportional relationship. if the

relationship could be proportional, what would be the constant of proportionality?
a. the sizes you can print a photo
b. the distance from which a lighthouse is
visible

Explanation:

Step1: Calculate the ratio for photo size table

For the photo size table:

• When width \(x = 2\) and height \(y=3\), the ratio \(\frac{y}{x}=\frac{3}{2} = 1.5\)
• When \(x = 4\) and \(y = 6\), the ratio \(\frac{y}{x}=\frac{6}{4}=1.5\)
• When \(x = 5\) and \(y = 7\), the ratio \(\frac{y}{x}=\frac{7}{5}=1.4\)
• Since the ratio is not constant for all pairs, the relationship is not proportional.

Step2: Calculate the ratio for lighthouse table

For the lighthouse table:

• When height \(x = 20\) and distance \(y = 6\), the ratio \(\frac{y}{x}=\frac{6}{20}=0.3\)
• When \(x = 45\) and \(y = 9\), the ratio \(\frac{y}{x}=\frac{9}{45}=0.2\)
• Since the ratio is not constant for all pairs, the relationship is not proportional.

Answer:

a. Not proportional.
b. Not proportional.