To determine which table of values represents a linear function, we need to check if the y-values change at a constant rate as the x-values change. This means for any two points, the change in y divided by the change in x (also known as the slope) should be constant.
Let's analyze each table:
A:
- (−2, 0), (1, 2), (5, 4), (8, 6)
- Changes in x: 1 - (−2) = 3, 5 - 1 = 4, 8 - 5 = 3
- Changes in y: 2 - 0 = 2, 4 - 2 = 2, 6 - 4 = 2
- The change in y is constant (2) but the change in x is not constant. Thus, this is not linear.
B:
- (1, 2), (2, 0), (3, −2), (5, −5)
- Changes in x: 2 - 1 = 1, 3 - 2 = 1, 5 - 3 = 2
- Changes in y: 0 - 2 = −2, −2 - 0 = −2, −5 - (−2) = −3
- The change in y is not constant, so this is also not linear.
C:
- (−5, −6), (−1, 0), (3, 6), (6, 9)
- Changes in x: (−1) - (−5) = 4, 3 - (−1) = 4, 6 - 3 = 3
- Changes in y: 0 - (−6) = 6, 6 - 0 = 6, 9 - 6 = 3
- The change in y is not constant; therefore, this is not linear.
D:
- (−5, −6), (−3, −4), (0, −1), (2, 11)
- Changes in x: (−3) - (−5) = 2, 0 - (−3) = 3, 2 - 0 = 2
- Changes in y: (−4) - (−6) = 2, (−1) - (−4) = 3, 11 - (−1) = 12
- The change in y is also not constant across the values, thus this is not linear.
Based on the analysis, none of the provided tables of values represent a linear function. If you have additional tables or values to consider, please share them, and I'll be happy to help.
3 answers