Question

Which set of ordered pairs satisfies a linear function?

A) {(-6, 6), (-3, 3), (0, 0), (3, 3), (6, 6)}
B) {(-2, 6), (-1,3), (0, 2), (1,3), (2, 6)}
C) {(-2, 6), (-1, 3), (0, 0), (1, -3), (2,-6)}
D) {(6,-2), (6, -1), (6,0), (6, 1), (6,2)

Answer 1

Sets A) {(-6, 6), (-3, 3), (0, 0), (3, 3), (6, 6)} and C) {(-2, 6), (-1, 3), (0, 0), (1, -3), (2,-6)} satisfy the conditions of a linear function, having consistent changes in y-values with respect to x that suggest positive and negative slopes respectively.

Step-by-step explanation:

To determine which set of ordered pairs satisfies a linear function, we must check if the relationship between the x- and y-values follows the format of a linear equation, which is typically y = mx + b, where m is the slope and b is the y-intercept.

Let's analyze each set:

1. A) {(-6, 6), (-3, 3), (0, 0), (3, 3), (6, 6)} - This shows a consistent relationship where y equals x, indicating a straight line with a positive slope.
2. B) {(-2, 6), (-1,3), (0, 2), (1,3), (2, 6)} - The y-values are not consistently changing with respect to x, which suggests this is not a linear function.
3. C) {(-2, 6), (-1, 3), (0, 0), (1, -3), (2,-6)} - The change in y-values is the negative of the change in x-values, displaying a negative slope and a linear relationship where y equals -x.
4. D) {(6,-2), (6, -1), (6,0), (6, 1), (6,2)} - All these ordered pairs have the same x-value, which represents a vertical line, not a function.

Considering these points, sets A) and C) satisfy the conditions of a linear function.