Do the data in the table represent a linear function? If so, write a rule for the function.
x -2 -1 0 1 2
y -7 1 8 17 25
yes; y = 8x+9
yes; y = 8x+8
yes; y = = 1/8 x+8
no
; the rate of change between the x-values and y-values is not constant.
To determine if the data in the table represent a linear function, we need to check if there is a constant \(\Delta y\) for a constant \(\Delta x\). Let's calculate the differences between consecutive y-values and x-values:
\(\Delta y_1 = 1 - (-7) = 8\)
\(\Delta y_2 = 8 - 1 = 7\)
\(\Delta y_3 = 17 - 8 = 9\)
\(\Delta y_4 = 25 - 17 = 8\)
The differences between the y-values are not constant, so the data in the table does not represent a linear function.