Question

Which table of values represents a linear function?

A
C
8
-3
-1
4
6
x
-8
-2
32
8
Y
9
8
5
4
Y
0
3
6
9
B
D
x
-1
2
5
8
x
2
4
6
8
y
-1
1
3
5
y
-8
-2
3
8

Answer 1

Option B represents a linear function because it shows a consistent ratio in changes of 'x' to changes in 'y', which reflects the linear equation form of 'y = mx + b' with a uniform slope.

Step-by-step explanation:

The question which table of values represents a linear function can be answered by understanding the characteristics of linear equations. A linear equation is an equation of a straight line and is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. In a linear function, for equal increments in x, the changes in y should also be constant, which reflects the uniform slope of the line.

Looking at each table of values provided, we need to identify the table where changes in x lead to consistent changes in y. Option B presents a table where for every increase of 3 in x, y increases by 2, which shows a consistent ratio and indicates a linear relationship. This reflects the behavior of the equation y = mx + b, making it the table that represents a linear function.