Question

Which set of ordered pairs (x, y) could represent a linear function?

Answer 1

Answer:

b

Step-by-step explanation:

every x value goes down by 2 every time, while every y value goes up by 4 every time.

Answer 2

Answer:

B

Step-by-step explanation:

In a linear function, the rate of change (slope) is constant.

Therefore, as the x-value increases or decreases by a constant, the y-values should also increase or decrease by a constant.

A = {(0, -1), (3, 3), (6, 6), (9, 9)}

• The x-values increase by 3 each time.
• The y-values increase by 4, 3, and 3.

Therefore, this is not a linear function as the increase in y-values is not constant compared to a constant increase in x-values.

B = {(-1, -6), (1, -2), (3, 2), (5, 6)}

• The x-values increase by 2 each time.
• The y-values increase by 4 each time.

Therefore, this is a linear function as the increase in x-values and y-values is constant.

C = {(-6, 6), (-4, 3), (2, -6), (4, -8)}

• The x-values increase by 2, 6, and 2.
• The y-values increase by -3, -9, and -2.

As the ratio of increases in x-values and y-values is not the same, this is not a linear function.

D = {(-2, 9), (1, 3), (3, -3), (6, -9)}

• The x-values increase by 3, 2, and 3.
• The y-values increase by -6 each time.

Therefore, this is not a linear function as the increase in x-values is not constant compared to a constant increase in y-values.