Write a rule for the linear function in the table.

x f/x
1 -7
2 -10
3 -13
4 -16

A. f(x) = -1/3x – 4
B. f(x) = 3x + 4
C. f(x) = –3x – 4
D. f(x) = x – 7
have no clue, would like some help

for each x, it decreases by 3 (-3x)

for x=0, then, it must be -4

f(x)=-3x-4

thank u so much bob!!!!

To find the rule for the linear function in the table, we can observe the relationship between the x-values and the corresponding f(x) values.

In this case, we can see that for each increase of 1 in the x-value, the f(x) value decreases by 3. This suggests that the slope of the linear function is -3, as each increase of 1 in x results in a decrease of 3 in f(x).

We can also see that when x = 1, f(x) = -7. This gives us the y-intercept of the linear function.

Putting this information together, the rule for the linear function in the table is:

f(x) = -3x - 4

Therefore, the correct answer is C. f(x) = -3x - 4.

To determine the rule for the linear function in the table, we need to observe the pattern between the x-values and the corresponding f(x) values.

One way to do this is to find the difference between consecutive x-values and f(x) values. Let's calculate the differences:

x: 1 2 3 4
f(x): -7 -10 -13 -16

Difference between x-values: 2 - 1 = 1 and 3 - 2 = 1 and 4 - 3 = 1
Difference between f(x) values: -10 - (-7) = -3 and -13 - (-10) = -3 and -16 - (-13) = -3

We can see that both the differences between x-values and f(x) values are constant, specifically -3. This indicates that the function has a constant rate of change, which is a characteristic of a linear function.

Now, let's use the given options to check which one matches the pattern:
A. f(x) = -1/3x - 4
B. f(x) = 3x + 4
C. f(x) = -3x - 4
D. f(x) = x - 7

To find the correct rule, we can substitute the x-values from the table into each option and check if the corresponding f(x) value matches the given values.

Substituting x = 1 into the options:
A. f(1) = -1/3(1) - 4 = -1/3 - 4 = -4 1/3
B. f(1) = 3(1) + 4 = 3 + 4 = 7
C. f(1) = -3(1) - 4 = -3 - 4 = -7
D. f(1) = (1) - 7 = -6

The corresponding f(1) value is -7 in the table, which matches option D.

Substituting x = 2 into the options:
A. f(2) = -1/3(2) - 4 = -2/3 - 4 = -4 2/3
B. f(2) = 3(2) + 4 = 6 + 4 = 10
C. f(2) = -3(2) - 4 = -6 - 4 = -10
D. f(2) = (2) - 7 = -5

The corresponding f(2) value is -10 in the table, which matches option C.

Similarly, we can substitute x = 3 and x = 4 into the options and check if the corresponding f(x) values match the table.

By checking all the options, we find that option C, f(x) = -3x - 4, matches all the given values in the table.

Therefore, the correct rule for the linear function in the table is: f(x) = -3x - 4.