8.)The data in the table illustrate a linear function.
x |-3| 0| 3|6|
y |-5|-3|-1|1|
A.) -3/2
B.)-2/3
C.)2/3
D.)3/2
C.)2/3
To determine if the data in the table represents a linear function, we need to check if there is a constant rate of change between the x-values and y-values. The rate of change is determined by taking the difference in y-values and dividing it by the difference in x-values.
Let's calculate the rate of change for each pair of points in the table:
Between x = -3 and x = 0:
Rate of change = (y2 - y1) / (x2 - x1)
Rate of change = (-3 - (-5)) / (0 - (-3))
Rate of change = (-3 + 5) / (0 + 3)
Rate of change = 2 / 3
Between x = 0 and x = 3:
Rate of change = (y2 - y1) / (x2 - x1)
Rate of change = (-1 - (-3)) / (3 - 0)
Rate of change = (-1 + 3) / (3 - 0)
Rate of change = 2 / 3
Between x = 3 and x = 6:
Rate of change = (y2 - y1) / (x2 - x1)
Rate of change = (1 - (-1)) / (6 - 3)
Rate of change = (1 + 1) / (6 - 3)
Rate of change = 2 / 3
We can see that the rate of change is the same for all pairs of points in the table, so the data represents a linear function. The common rate of change is 2/3.
Therefore, the answer is C) 2/3.
To determine if the data in the table illustrates a linear function, we need to check if there is a constant rate of change between the x-values and the y-values.
Let's calculate the rate of change between two consecutive x-values and y-values:
Between x = -3 and x = 0:
y = -5 and y = -3
Rate of change = change in y / change in x
= (-3 - (-5)) / (0 - (-3))
= 2 / 3
Between x = 0 and x = 3:
y = -3 and y = -1
Rate of change = change in y / change in x
= (-1 - (-3)) / (3 - 0)
= 2 / 3
Between x = 3 and x = 6:
y = -1 and y = 1
Rate of change = change in y / change in x
= (1 - (-1)) / (6 - 3)
= 2 / 3
Since the rate of change between the x-values and the y-values is constant and equal to 2/3, the data in the table illustrates a linear function.
Therefore, the answer is C.) 2/3.