Question

Which table represents a linear function?

Answer 1

Answer: Table 3

A table of values x and y represents a linear function, 

if the change in x is always proportional with the change in y:


For example:

x changes from 1 to 2, y changes from -3 to -5

that is, a change of 1 in the x-es, is a change of +2 in the y's.


x changes from 2 to 4, y changes from -5 to -9
that is, a change of 2 in x, is a change of +4 in the y's.

1, 2  and 2, 4 are proportional




Another way we can check that Table 3 is the only one representing a linear function, is the constant change in y:

as x takes the values : 1, 2, 3, 4, y becomes -3, -5, -7, -9

that is, a constant change of 1 in the x-es, means a constant change of +2 in the y's

Answer 2

The table 3 represents the linear function between $x$ and $y$.

Further explanation:

The relation is defined as the relationship between the input values and output values.

In the interval $\left( {x,y} \right)$ the first value represents the $x$ and the second value is $y$.

The x coordinates are the domain of the function and the y coordinates are the range of the function.

The linear equation with slope $m$ and y-intercept $c$ is given as follows.

$\boxed{y = mx + c}$

Explanation:

In table 1 the value of x and y are not in linear relation. Table 1 is not correct.

In table 2 the value of x and y are not in linear relation. Table 2 is not correct.

In table 3 as x increases the value of y also increases in a same proportion. Therefore x and y are in a linear relationship. Table 3 is correct.

In table 2 the value of x and y are not in linear relation. Table 2 is not 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: linear function, relation table, same relation, set, set of values, set of numbers, coordinates, x-coordinate, y-coordinate.