Answer:
To fill in the table values, we need to understand the graph provided:
```
y-axis
^
|
| .
| .
| .
|.
+-----------------> x-axis
```
From the graph:
- For the point (1, -8), the value of the function is -8.
- For the point (2, -5), the value of the function is -5.
- For the point (3, -2), the value of the function is -2.
- For the point (4, R), the value of the function is not given.
So, based on the graph, the table looks like this:
| x | y |
|-------|-------|
| 1 | -8 |
| 2 | -5 |
| 3 | -2 |
| 4 | R |
To find the value of R, we need to understand the pattern or behavior of the graph. From the given points, we can see that as x increases by 1, y increases by 3. Therefore, the common difference is 3.
Now, let's find the value of R:
From x = 3 to x = 4, there's a difference of 1.
If we add 3 to y (from the point (3, -2)), we get -2 + 3 = 1.
So, the value of R would be 1.
Therefore, the completed table is:
| x | y |
|-------|-------|
| 1 | -8 |
| 2 | -5 |
| 3 | -2 |
| 4 | 1 |
Common difference: 3
Explicit formula: \( y = -3x + 5 \)
