please help! I can't figure out the function rule for a table that says

for the given values it looks like

y = -3x + 9

you gotta graph

you gotta graph

To determine the function rule for the given table, we need to find the relationship between the values of x and y. Let's analyze the pattern:

When x increases by 1, y decreases by 3. This can be observed between the first two rows (x=0 and x=1), as well as the third and fourth rows (x=4 and x=5).

Based on this pattern, we can conclude that the function rule is a linear relationship. In other words, the function can be written in the form of y = mx + b, where m represents the slope and b represents the y-intercept.

To find the slope (m), we can use any two points from the table. Let's choose the first and second rows:

For x=0 and x=1:
y = 9 and y = 6

Using the slope formula (m = (y2 - y1) / (x2 - x1)), we can calculate the slope (m):

m = (6 - 9) / (1 - 0)
m = -3 / 1
m = -3

Now that we have the slope, we can determine the y-intercept (b). Let's use the first point from the table (x=0, y=9) and substitute the values into the equation y = mx + b:

9 = -3(0) + b
9 = b

So, the y-intercept (b) is 9.

Now, we can write the function rule based on the slope and y-intercept we found:

y = -3x + 9

Therefore, the function rule for the given table is y = -3x + 9.