Question

Which graph shows a proportional relationship?

Answer 1

The first picture, second picture,fourth picture represents proportional relationship.

Further explanation:

Explanation:

The points in the first picture are $\left( {0,0} \right), \left( {2,1} \right),\left( {4,2} \right)$ and $\left( {6,3} \right).$

The slopes between the points can be obtained as follows,

$\begin{aligned}m &\frac{{1 - 0}}{{2 - 0}}\\&= \frac{1}{2}\\\end{aligned}$

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

$\begin{aligned}m&= \frac{{3 - 2}}{{6 - 4}}\\&= \frac{1}{2}\\\end{aligned}$

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

The points in the second picture are $\left( {0,2} \right), \left( {1,3} \right),\left( {2,4} \right)$ and $\left( {3,5} \right).$

The slopes between the points can be obtained as follows,

$\begin{aligned}m&= \frac{{3 - 2}}{{1 - 0}}\\&= 1\\\end{aligned}$

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

$\begin{aligned}m&=\frac{{5 - 4}}{{3 - 2}}\\&= 1\\\end{aligned}$

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 $\left( {0,4} \right), \left( {1,3} \right),\left( {2,2} \right)$ and $\left( {3,1} \right).$

The slopes between the points can be obtained as follows,

$\begin{aligned}m&= \frac{{3 - 4}}{{1 - 0}}\\&= - 1\\\end{aligned}$

The slope is negative. Therefore, in the third picture x and y are not in a proportional relationship.

The points in the fourth picture are $\left( {2,0} \right), \left( {3,1} \right),\left( {4,2} \right)$ and $\left( {5,3} \right).$

The slopes between the points can be obtained as follows,

$\begin{aligned}m&= \frac{{1 - 0}}{{3 - 2}}\\&= 1\\\end{aligned}$

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

$\begin{aligned}m&= \frac{{3 - 2}}{{5 - 4}}\\&= 1\\\end{aligned}$

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

The first picture, second picture,fourth picture represents proportional relationship.

Learn more:

1. Learn more about inverse of the function 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, set, set of values, set of numbers, coordinates, x-coordinate, y-coordinate.

Answer 2

The first and the second and the last one