Question

Is the set of numbers represent a linear function ? (2,5), (-4,9), (6,-3),(8,3) and (-4,4)

Answer 1

To determine if the set of numbers represents a linear function, we need to check if there is a constant rate of change between the input values and output values.

Let's calculate the rate of change between the pairs of points:

- Between (2, 5) and (-4, 9):
Rate of change = (9 - 5) / (-4 - 2) = 4 / (-6) = -2/3

- Between (-4, 9) and (6, -3):
Rate of change = (-3 - 9) / (6 - (-4)) = -12 / 10 = -6/5

- Between (6, -3) and (8, 3):
Rate of change = (3 - (-3)) / (8 - 6) = 6 / 2 = 3

- Between (8, 3) and (-4, 4):
Rate of change = (4 - 3) / (-4 - 8) = 1 / (-12) = -1/12

As we can see, the rate of change between the pairs of points is not constant. Therefore, the set of numbers does not represent a linear function.