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
anyone im taking the test rn
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 the corresponding y-values.
We can calculate the rate of change using the formula:
Rate of change = (change in y) / (change in x)
Let's calculate the rate of change between the first two points:
Rate of change = (y2 - y1) / (x2 - x1)
= (-3 - (-5)) / (0 - (-3))
= (-3 + 5) / (0 + 3)
= 2 / 3
Now, let's calculate the rate of change between the next two points:
Rate of change = (y3 - y2) / (x3 - x2)
= (-1 - (-3)) / (3 - 0)
= (-1 + 3) / (3 - 0)
= 2 / 3
Finally, let's calculate the rate of change between the last two points:
Rate of change = (y4 - y3) / (x4 - x3)
= (1 - (-1)) / (6 - 3)
= (1 + 1) / (6 - 3)
= 2 / 3
Since the rate of change is the same for all pairs of points, it shows that the data in the table represents a linear function.
Therefore, the correct answer is 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 the y-values.
Let's calculate the rate of change between each pair of x and y values:
Rate of change = change in y / change in x
For the first pair of values (-3, -5) and (0, -3):
Change in y = -3 - (-5) = 2
Change in x = 0 - (-3) = 3
Rate of change = 2/3
For the second pair of values (0, -3) and (3, -1):
Change in y = -1 - (-3) = 2
Change in x = 3 - 0 = 3
Rate of change = 2/3
For the third pair of values (3, -1) and (6, 1):
Change in y = 1 - (-1) = 2
Change in x = 6 - 3 = 3
Rate of change = 2/3
Since the rate of change between each pair of values is the same (2/3), we can conclude that the data in the table represents a linear function.
Now, let's find the slope of the linear function. The slope represents the rate of change between the x-values and the y-values. We can choose any two points from the table to calculate the slope.
Let's use the first and last points (-3, -5) and (6, 1):
Slope = (change in y) / (change in x)
= (1 - (-5)) / (6 - (-3))
= 6 / 9
= 2/3
Therefore, the slope of the linear function is 2/3.
Out of the given options, the correct answer is C) 2/3.