Question

(3.) Which graph shows a proportional relationship?

Answer 1

(3). The second picture represents proportional relationship.

(4). The proportional relationship with $\dfrac{4}{5}$ is $\boxed{\frac{{20}}{{25}}}$. Option (B) is correct.

Further explanation:

Explanation:

The points in the first picture are $\left( {1,1} \right), \left( {3,4} \right),\left( {5,7} \right)$ and $\left( {6,8.25} \right).$

The slopes between the points can be obtained as follows,

$\begin{aligned}m&=\frac{{4 - 1}}{{3 - 1}}\\&=\frac{3}{2}\\\end{aligned}$

$\begin{aligned}m&=\frac{{7 - 4}}{{5 - 3}}\\&= \frac{3}{2}\\\end{aligned}$

$\begin{aligned}m&= \frac{{8.25 - 7}}{{6 - 5}}\\&= \frac{{1.25}}{1}\\\end{aligned}$

The slopes between the points are not equal. Therefore, in the first picture x and y are not in a proportional relationship.

The points in the second picture arec$\left( {1,2} \right), \left( {2,4} \right),\left( {4,8} \right)$ and $\left( {6,10} \right).$

The slopes between the points can be obtained as follows,

$\begin{aligned}m&= \frac{{4 - 2}}{{2 - 1}}\\&= 2\\\end{aligned}$

$\begin{aligned}m&= \frac{{8 - 4}}{{4 - 2}}\\&= 2\\\end{aligned}$

$\begin{aligned}m&=\frac{{12 - 8}}{{6 - 4}}\\&= 2\\\end{aligned}$

The slopes between the points are equal. Therefore, in the second picture x and y are in a proportional relationship.

The points in the third picture are $\left( {0,0} \right), \left( {2,5} \right),\left( {4,8} \right)$ and $\left( {6,10} \right).$

The slopes between the points can be obtained as follows,

$\begin{aligned}m&= \frac{{5 - 0}}{{2 - 0}}\\&= \frac{5}{2}\\\end{aligned}$

$\begin{aligned}m&=\frac{{8 - 5}}{{4 - 2}}\\&=\frac{3}{2}\\\end{aligned}$

The slopes between the points are not equal. Therefore, in the third picture x and y are not in a proportional relationship.

The points in the first picture are $\left( {1,12} \right), \left( {2,10} \right),\left( {5,4} \right)$ and $\left( {6,2} \right).$

The slopes between the points can be obtained as follows,

$\begin{aligned}m&=\frac{{10 - 12}}{{3 - 1}}\\&= \frac{{ - 2}}{1}\\\end{aligned}$

$\begin{aligned}m&= \frac{{4 - 10}}{{5 - 2}}\\&= - 2\\\end{aligned}$

$\begin{aligned}m&= \frac{{2 - 4}}{{6 - 5}}\\&= \frac{{ - 2}}{1}\\\end{aligned}$

The slopes between the points are equal but the slope is negative. Therefore, in the fourth picture x and y are not in a proportional relationship.

Part (4)

The ratio of red candies to green candies in a bag is $\dfrac{4}{5}.$

In option (A)

The ratio can be calculated as follows,

${\text{Ratio}} = \dfrac{{16}}{{25}}$

In option (B)

The ratio can be calculated as follows,

$\begin{aligned}{\text{Ratio}}&= \frac{{20}}{{25}}\\&=\frac{4}{5}\\\end{aligned}$

In option (C)

The ratio can be calculated as follows,

$\begin{aligned}{\text{Ratio}}&= \frac{{20}}{{35}}\\&= \frac{4}{7}\\\end{aligned}$

In option (D)

The ratio can be calculated as follows,

$\begin{aligned}{\text{Ratio}}&=\frac{{24}}{{32}}\\&= \frac{3}{4}\\\end{aligned}$

The proportional relationship with $\dfrac{4}{5}$ is $\boxed{\frac{{20}}{{25}}}$. Option (B) is correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Ratio and proportion

Keywords: function, First picture, second picture, proportional relationship, ratio, slope, green candies, bag, red candies, 4/5, same relation, set, set of values, set of numbers, coordinates, x-coordinate, y-coordinate.