Question

Which table shows a proportional relationship between a and b

Answer 1

Answer:

the answer in the attached figure

Step-by-step explanation:

we know that

A relationship between two variables, a, and b, represent a proportional relationship if it can be expressed in the form $a/b=k$

we're going to verify all the cases

Table A

$(3,9),(4,12),(5,20)$

$9/3=3$

$12/4=3$

$20/5=4$

The table A does not represent a proportional relationship

Table B

$(20,25),(24,30),(32,40)$

$25/20=1.25$

$30/24=1.25$

$40/32=1.25$    

The table B  represents a proportional relationship between a and b

Table C

$(4,12),(5,15),(6,24)$

$12/4=3$

$15/5=3$

$24/6=4$

The table C does not represent a proportional relationship

Table D

$(3,4),(6,9),(12,16)$

$12/4=3$

$15/5=3$

$24/6=4$

The table D does not represent a proportional relationship

therefore

the answer in the attached figure

Answer 2

The table (B) shows the proportional relationship between a and b.

Further Explanation:

The proportional relationship between any two numbers can be expressed as follows,

$\boxed{\dfrac{a}{b} = c}$

Here, a and b are the two numbers and c is the proportional ratio.

Explanation:

In Table A the values are $\left( {3,9}\right),\left({4,12}\right)$ and $\left( {5,20}\right).$

The ratios of a and b can be calculated as follows,

$\dfrac{3}{9} &= \dfrac{1}{3}\dfrac{4}{{12}}&=\dfrac{1}{3}\dfrac{5}{{20}}&= \dfrac{1}{4}$

The ratios of all the set of numbers are not equal. Therefore, a and b are not in a proportional relationship in Table (A).

In Table B the values are $\left( {20,25} \right),\left( {24,30} \right)$ and $\left( {32,40}\right).$

The ratios of a and b can be calculated as follows,

$\dfrac{{20}}{{25}}&=\ddfrac{4}{5}\dfrac{{24}}{{30}}&= \frac{4}{5}\dfrac{{32}}{{40}} &=\dfrac{4}{5}$

The ratios of all the set of numbers are equal. Therefore, a and b are in a proportional relationship in Table (B).

In Table C the values are $\left( {4,12}\right),\left( {5,15}\right)$ and $\left( {6,24}\right).$

The ratios of a and b can be calculated as follows,

$\dfrac{4}{12}&=\dfrac{1}{3}\dfrac{5}{{15}}&=\dfrac{1}{3}\dfrac{6}{{24}}&= \dfrac{1}{4}$

The ratios of all the set of numbers are not equal. Therefore, a and b are not in a proportional relationship in Table (C).

In Table D the values are $\left({3,4}\right),\left( {6,9}\right)$ and $\left({12,16}\right).$

The ratios of a and b can be calculated as follows,

$\dfrac{3}{4}&=\dfrac{3}{4}\dfrac{6}{{9}}&=\dfrac{2}{3}\dfrac{12}{{16}}&=\dfrac{3}{4}$

The ratios of all the set of numbers are not equal. Therefore, a and b are not in a proportional relationship in Table (D).

Table (A) is not correct.

Table (B) is correct.

Table (C) is not correct.

Table (D) is not correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Ratio and Proportion

Keywords: proportional relationship, shows, a, b, ratio, table, fraction.