Question

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 part a

For a proportional relationship, the ratio of \(y\) (height) to \(x\) (width) should be constant.
For \(x = 2,y=3\), the ratio is \(\frac{3}{2}=1.5\).
For \(x = 4,y = 6\), the ratio is \(\frac{6}{4}=1.5\).
For \(x=5,y = 7\), the ratio is \(\frac{7}{5}=1.4\).
Since \(\frac{3}{2}=\frac{6}{4}
eq\frac{7}{5}\), the relationship is not proportional.

Step2: Check proportionality for part b

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

Answer:

a. The relationship is not proportional.
b. The relationship is not proportional.