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:
- Learn more about inverse of the function https://brainly.com/question/1632445.
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- Learn more about range and domain of the function https://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.
