Question

The table of values shown below represents a linear function. Which of these points could also be an ordered pair in the table, and why? x 0 3 6 9 12 y 3 7 11 15 19 a (18, 27), because the rate of change of the function is Three-fourths b (18, 27), because the rate of change of the function is Four-thirds c (27, 18), because the rate of change of the function is Three-fourths d (27, 18), because the rate of change of the function is Four-thirds

Answer 1

The rate of change of a linear function is constant and is equal to the slope of the line.

To find the slope of the line, we can use any two points from the table. Let's use the first and last points:

slope = (19 - 3) / (12 - 0) = 16 / 12 = 4 / 3

This means that the function has a rate of change of 4/3, or 1.33.

Now, let's check each of the answer choices:

a) (18, 27) - This point is not in the table and does not have the correct coordinates.

b) (18, 27) - This point is not in the table and does not have the correct coordinates.

c) (27, 18) - This point is not in the table and does not have the correct coordinates.

d) (27, 18) - This point is not in the table and does not have the correct coordinates.

None of these points are in the table, and therefore none of them could be an ordered pair in the table.