Question

review problems

1. select all the pieces of information that would tell you ( x ) and ( y ) have a propo

relationship. let ( y ) represent the distance in feet (ft.) between a rock and a t
current position, and let ( x ) represent the time in minutes (min.) the turtle has
moving for.
( square y = 3x )
( square ) the turtle walks in a circle around the rock.
( square ) the turtle walks away from the rock at a constant rate.
( square ) after 4 min., the turtle has walked 12 ft. away from the rock.
( square ) 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 proportionalit

a. the sizes you can print a photo

b. the distance from which a lighthouse is
visible

Explanation:

Step1: Check proportionality for photo sizes

For a proportional relationship, the ratio \(\frac{y}{x}\) (height/width) should be constant.
For the photo size table:

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

Step2: Check proportionality for lighthouse data

For the lighthouse table:

• When \(x = 20,y=6\), \(\frac{y}{x}=\frac{6}{20}=0.3\)
• When \(x = 45,y = 9\), \(\frac{y}{x}=\frac{9}{45}=0.2\)
• Since the ratio is not constant (0.3 vs 0.2), the relationship is not proportional.

Answer:

a. The relationship for photo sizes is not proportional.
b. The relationship for lighthouse data is not proportional.