what function rule represents the data in the table?
X |-3 | -2 | -1 | 0 | 1
Y | -17 |-14 | -11 | -8 |-5
A: y=-3x-8
B: y=1/3x-8
C: y=3x-8
D: y=1/3x+8
C: y=3x-8
To find the function rule that represents the data in the table, we can observe the relationship between the values of x and y.
Let's start by calculating the slope between two consecutive points. Taking the first two points (-3, -17) and (-2, -14):
Slope = (change in y) / (change in x)
Slope = (-14 - (-17)) / (-2 - (-3))
Slope = (-14 + 17) / (-2 + 3)
Slope = 3/1 = 3
Now, let's check if this slope remains constant for other pairs of points:
(-2, -14) and (-1, -11): Slope = (change in y) / (change in x) = 3
(-1, -11) and (0, -8): Slope = (change in y) / (change in x) = 3
(0, -8) and (1, -5): Slope = (change in y) / (change in x) = 3
Since the slope remains constant for all pairs of points, we know that the function is linear, and the coefficient of x will be 3.
Now, we need to find the y-intercept, which is the value of y when x=0. From the table, when x=0, y=-8.
Putting all this information together, the function rule that represents the data in the table is y = 3x - 8.
Therefore, the correct option is C: y = 3x - 8.