Question

Please help me determine the constant rate of change for both of these tables. 5 and 6 please.

Answer 1

The constant rate of change between two given points on the function is given by,

`R=(\Delta y)/(\Delta x)`

Since it is already mentioned that the rate of change is constant, so we don't need to check that. And the constant rate of change can be evaluated using any 2 pair of points from the table.

5.

Consider the first two points, (1,6) and (2,12).

The constant rate of change is calculated as,

`\begin{gathered} R=(12-6)/(2-1) \\ R=(6)/(1) \\ R=6 \end{gathered}`

Thus, the constant rate of change is 6 units in 'y' per unit change in 'x'.

6.

Consider the first two points, (2,18) and (4,36).

The constant rate of change is calculated as,

`\begin{gathered} R=(36-18)/(4-2) \\ R=(18)/(2) \\ R=(9\cdot2)/(2) \\ R=9 \end{gathered}`

Thus, the constant rate of change is 9 units in 'y' per unit change in 'x'.