Question

south carolina
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.

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: Check proportionality for photo sizes

For a proportional relationship, \(\frac{y}{x}\) (where \(y\) is height and \(x\) is width) should be constant.
For \(x = 2,y=3\), \(\frac{y}{x}=\frac{3}{2}=1.5\)
For \(x = 4,y = 6\), \(\frac{y}{x}=\frac{6}{4}=1.5\)
For \(x=5,y = 7\), \(\frac{y}{x}=\frac{7}{5}=1.4\)
Since \(\frac{7}{5}
eq1.5\), the photo - size relationship is not proportional.

Step2: Check proportionality for lighthouse data

For a proportional relationship, \(\frac{y}{x}\) (where \(y\) is distance and \(x\) is height) should be constant.
For \(x = 20,y=6\), \(\frac{y}{x}=\frac{6}{20}=0.3\)
For \(x = 45,y = 9\), \(\frac{y}{x}=\frac{9}{45}=0.2\)
Since \(0.3
eq0.2\), the lighthouse - distance relationship is not proportional.

Answer:

a. The table for the sizes you can print a photo does not represent a proportional relationship.
b. The table for the distance from which a lighthouse is visible does not represent a proportional relationship.