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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
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
The table 3 represents the linear function between [tex]x[/tex] and [tex]y[/tex].
Further explanation:
The relation is defined as the relationship between the input values and output values.
In the interval [tex]\left( {x,y} \right)[/tex] the first value represents the [tex]x[/tex] and the second value is [tex]y[/tex].
The x coordinates are the domain of the function and the y coordinates are the range of the function.
The linear equation with slope [tex]m[/tex] and y-intercept [tex]c[/tex] is given as follows.
[tex]\boxed{y = mx + c}[/tex]
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 https://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.
