(3). The second picture represents proportional relationship.
(4). The proportional relationship with
is
. Option (B) is correct.
Further explanation:
Explanation:
The points in the first picture are
and ![\left( {6,8.25} \right).](https://tex.z-dn.net/?f=%5Cleft%28%20%7B6%2C8.25%7D%20%5Cright%29.)
The slopes between the points can be obtained as follows,
![\begin{aligned}m&=\frac{{4 - 1}}{{3 - 1}}\\&=\frac{3}{2}\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%5Cfrac%7B%7B4%20-%201%7D%7D%7B%7B3%20-%201%7D%7D%5C%5C%26%3D%5Cfrac%7B3%7D%7B2%7D%5C%5C%5Cend%7Baligned%7D)
![\begin{aligned}m&=\frac{{7 - 4}}{{5 - 3}}\\&= \frac{3}{2}\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%5Cfrac%7B%7B7%20-%204%7D%7D%7B%7B5%20-%203%7D%7D%5C%5C%26%3D%20%5Cfrac%7B3%7D%7B2%7D%5C%5C%5Cend%7Baligned%7D)
![\begin{aligned}m&= \frac{{8.25 - 7}}{{6 - 5}}\\&= \frac{{1.25}}{1}\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%20%5Cfrac%7B%7B8.25%20-%207%7D%7D%7B%7B6%20-%205%7D%7D%5C%5C%26%3D%20%5Cfrac%7B%7B1.25%7D%7D%7B1%7D%5C%5C%5Cend%7Baligned%7D)
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
and ![\left( {6,10} \right).](https://tex.z-dn.net/?f=%5Cleft%28%20%7B6%2C10%7D%20%5Cright%29.)
The slopes between the points can be obtained as follows,
![\begin{aligned}m&= \frac{{4 - 2}}{{2 - 1}}\\&= 2\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%20%5Cfrac%7B%7B4%20-%202%7D%7D%7B%7B2%20-%201%7D%7D%5C%5C%26%3D%202%5C%5C%5Cend%7Baligned%7D)
![\begin{aligned}m&= \frac{{8 - 4}}{{4 - 2}}\\&= 2\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%20%5Cfrac%7B%7B8%20-%204%7D%7D%7B%7B4%20-%202%7D%7D%5C%5C%26%3D%202%5C%5C%5Cend%7Baligned%7D)
![\begin{aligned}m&=\frac{{12 - 8}}{{6 - 4}}\\&= 2\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%5Cfrac%7B%7B12%20-%208%7D%7D%7B%7B6%20-%204%7D%7D%5C%5C%26%3D%202%5C%5C%5Cend%7Baligned%7D)
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
and ![\left( {6,10} \right).](https://tex.z-dn.net/?f=%5Cleft%28%20%7B6%2C10%7D%20%5Cright%29.)
The slopes between the points can be obtained as follows,
![\begin{aligned}m&= \frac{{5 - 0}}{{2 - 0}}\\&= \frac{5}{2}\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%20%5Cfrac%7B%7B5%20-%200%7D%7D%7B%7B2%20-%200%7D%7D%5C%5C%26%3D%20%5Cfrac%7B5%7D%7B2%7D%5C%5C%5Cend%7Baligned%7D)
![\begin{aligned}m&=\frac{{8 - 5}}{{4 - 2}}\\&=\frac{3}{2}\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%5Cfrac%7B%7B8%20-%205%7D%7D%7B%7B4%20-%202%7D%7D%5C%5C%26%3D%5Cfrac%7B3%7D%7B2%7D%5C%5C%5Cend%7Baligned%7D)
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
and ![\left( {6,2} \right).](https://tex.z-dn.net/?f=%5Cleft%28%20%7B6%2C2%7D%20%5Cright%29.)
The slopes between the points can be obtained as follows,
![\begin{aligned}m&=\frac{{10 - 12}}{{3 - 1}}\\&= \frac{{ - 2}}{1}\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%5Cfrac%7B%7B10%20-%2012%7D%7D%7B%7B3%20-%201%7D%7D%5C%5C%26%3D%20%5Cfrac%7B%7B%20-%202%7D%7D%7B1%7D%5C%5C%5Cend%7Baligned%7D)
![\begin{aligned}m&= \frac{{4 - 10}}{{5 - 2}}\\&= - 2\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%20%5Cfrac%7B%7B4%20-%2010%7D%7D%7B%7B5%20-%202%7D%7D%5C%5C%26%3D%20-%202%5C%5C%5Cend%7Baligned%7D)
![\begin{aligned}m&= \frac{{2 - 4}}{{6 - 5}}\\&= \frac{{ - 2}}{1}\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%26%3D%20%5Cfrac%7B%7B2%20-%204%7D%7D%7B%7B6%20-%205%7D%7D%5C%5C%26%3D%20%5Cfrac%7B%7B%20-%202%7D%7D%7B1%7D%5C%5C%5Cend%7Baligned%7D)
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}.](https://tex.z-dn.net/?f=%5Cdfrac%7B4%7D%7B5%7D.)
In option (A)
The ratio can be calculated as follows,
![{\text{Ratio}} = \dfrac{{16}}{{25}}](https://tex.z-dn.net/?f=%7B%5Ctext%7BRatio%7D%7D%20%3D%20%5Cdfrac%7B%7B16%7D%7D%7B%7B25%7D%7D)
In option (B)
The ratio can be calculated as follows,
![\begin{aligned}{\text{Ratio}}&= \frac{{20}}{{25}}\\&=\frac{4}{5}\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%7B%5Ctext%7BRatio%7D%7D%26%3D%20%5Cfrac%7B%7B20%7D%7D%7B%7B25%7D%7D%5C%5C%26%3D%5Cfrac%7B4%7D%7B5%7D%5C%5C%5Cend%7Baligned%7D)
In option (C)
The ratio can be calculated as follows,
![\begin{aligned}{\text{Ratio}}&= \frac{{20}}{{35}}\\&= \frac{4}{7}\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%7B%5Ctext%7BRatio%7D%7D%26%3D%20%5Cfrac%7B%7B20%7D%7D%7B%7B35%7D%7D%5C%5C%26%3D%20%5Cfrac%7B4%7D%7B7%7D%5C%5C%5Cend%7Baligned%7D)
In option (D)
The ratio can be calculated as follows,
![\begin{aligned}{\text{Ratio}}&=\frac{{24}}{{32}}\\&= \frac{3}{4}\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%7B%5Ctext%7BRatio%7D%7D%26%3D%5Cfrac%7B%7B24%7D%7D%7B%7B32%7D%7D%5C%5C%26%3D%20%5Cfrac%7B3%7D%7B4%7D%5C%5C%5Cend%7Baligned%7D)
The proportional relationship with
is
. Option (B) is correct.
Learn more:
- Learn more about inverse of the functionhttps://brainly.com/question/1632445.
- Learn more about equation of circle brainly.com/question/1506955.
- 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.