Short answer
Completed table:
| Column X | Column Y |
|---|---|
| -4 | 5 |
| -3 | 4.5 |
| -2 | 4 |
| -1 | 3.5 |
| 0 | 3 |
| 1 | 2.5 |
| 2 | 2 |
| 3 | 1.5 |
| 4 | 1 |
General rule:
\[ y=3-\frac{x}{2} \]
or equivalently:
\[ y=\frac{6-x}{2}=-0.5x+3 \]
How to get the rule
- Each time \(x\) increases by 1, \(y\) decreases by \(0.5\).
- At \(x=0\), the value is \(y=3\), so the starting value is 3.
- Therefore:
\[ y=3-0.5x \]
Check with a table value: when \(x=-4\),
\[ y=3-0.5(-4)=3+2=5 \]
That matches the table.
Part b: test with \(x=3\) and \(x=4\)
\[ x=3:\quad y=3-0.5(3)=3-1.5=1.5 \]
\[ x=4:\quad y=3-0.5(4)=3-2=1 \]
These values continue the pattern: from \(x=2,\ y=2\), the next \(y\)-values go down by \(0.5\) each time: \(2,\ 1.5,\ 1\). Since the rule gives every visible table value and keeps the same constant change, it is correct.
