determine whether the table could represent a proportional relationship. if the relationship could be…

determine whether the table could represent a proportional relationship. if the relationship could be proportional, what would be the constant of proportionality? if the relationship cannot be proportional, explain how you know.\na. the measurements of books on a shelf.

determine whether the table could represent a proportional relationship. if the relationship could be proportional, what would be the constant of proportionality? if the relationship cannot be proportional, explain how you know.\na. the measurements of books on a shelf.

Answer

Explanation:

Step1: Calculate the ratios

For the first pair: $\frac{15}{10} = 1.5$ For the second pair: $\frac{13}{9}\approx1.44$ For the third pair: $\frac{11}{7}\approx1.57$ For the fourth pair: $\frac{5}{4} = 1.25$

Step2: Check for constant ratio

Since the ratios $\frac{length}{width}$ ($1.5$, $1.44$, $1.57$, $1.25$) are not equal.

Answer:

The relationship cannot be proportional. Because when calculating the ratios of length to width for each pair of values ($\frac{15}{10}=1.5$, $\frac{13}{9}\approx1.44$, $\frac{11}{7}\approx1.57$, $\frac{5}{4} = 1.25$), the ratios are not constant. In a proportional relationship, the ratio between the two quantities (in this case, length and width) must be constant.