Which function rule represents the data in the table?
x -3 -2 -1 10 1
y 1 -2 -5 -8 -11
y=-3x - 8
y=1/3x - 8
y=1/3x + 8
y=3x + 8
y=-3x - 8
To determine the function rule that represents the data in the table, we need to observe the relationship between the x-values and the corresponding y-values.
If we look at the y-values, we can see that they decrease by 3 each time the x-value increases by 1. This indicates a linear relationship.
To find the equation of a linear function, we can use the slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept.
Let's calculate the slope using two points from the table:
Using (x = -2, y = -2) and (x = -1, y = -5):
m = (y₂ - y₁) / (x₂ - x₁)
= (-5 - (-2)) / (-1 - (-2))
= (-5 + 2) / (-1 + 2)
= -3 / 1
= -3
Now, we can substitute the slope and one of the points back into the slope-intercept form to find the equation.
Using the point (x = -2, y = -2), we have:
-2 = (-3)(-2) + b
-2 = 6 + b
b = -2 - 6
b = -8
Therefore, the equation that represents the data in the table is y = -3x - 8.
So, the correct function rule is y = -3x - 8.