Function tables and the coordinate plane worksheets | Worsheets library - Free Printable

Let's solve the problem step by step.

We are given two function rules and need to:

1. Complete the function tables by calculating the corresponding $ y $-values using the given rule.
2. Write the ordered pairs $ (x, y) $ for each row.
3. Plot the points on the coordinate plane.

---

🔹 First Rule: $ y = 2x $

We'll plug in each $ x $-value into the equation $ y = 2x $.

| $ x $ | $ y = 2x $ | Ordered Pairs |
|--------|-------------|----------------|
| -2 | $ 2(-2) = -4 $ | (-2, -4) |
| -1 | $ 2(-1) = -2 $ | (-1, -2) |
| 0 | $ 2(0) = 0 $ | (0, 0) |
| 1 | $ 2(1) = 2 $ | (1, 2) |
| 2 | $ 2(2) = 4 $ | (2, 4) |

✔ Completed Table 1:
```
x y Ordered Pairs
-2 -4 (-2, -4)
-1 -2 (-1, -2)
0 0 (0, 0)
1 2 (1, 2)
2 4 (2, 4)
```

Now, plot these points on the top coordinate grid:
- Start at the origin (0,0).
- Plot each point: (-2,-4), (-1,-2), (0,0), (1,2), (2,4).
- Connect them with a straight line since this is a linear function.

---

🔹 Second Rule: $ y = x + 5 $

Now use the rule $ y = x + 5 $.

| $ x $ | $ y = x + 5 $ | Ordered Pairs |
|--------|------------------|----------------|
| -2 | $ -2 + 5 = 3 $ | (-2, 3) |
| -1 | $ -1 + 5 = 4 $ | (-1, 4) |
| 0 | $ 0 + 5 = 5 $ | (0, 5) |
| 1 | $ 1 + 5 = 6 $ | (1, 6) |
| 2 | $ 2 + 5 = 7 $ | (2, 7) |

✔ Completed Table 2:
```
x y Ordered Pairs
-2 3 (-2, 3)
-1 4 (-1, 4)
0 5 (0, 5)
1 6 (1, 6)
2 7 (2, 7)
```

Now, plot these points on the bottom coordinate grid:
- Plot: (-2,3), (-1,4), (0,5), (1,6), (2,7).
- These also form a straight line with slope 1 and y-intercept 5.

---

✔ Final Answer Summary

#### Rule: $ y = 2x $
| x | y | Ordered Pairs |
|---|---|----------------|
| -2 | -4 | (-2, -4) |
| -1 | -2 | (-1, -2) |
| 0 | 0 | (0, 0) |
| 1 | 2 | (1, 2) |
| 2 | 4 | (2, 4) |

#### Rule: $ y = x + 5 $
| x | y | Ordered Pairs |
|---|---|----------------|
| -2 | 3 | (-2, 3) |
| -1 | 4 | (-1, 4) |
| 0 | 5 | (0, 5) |
| 1 | 6 | (1, 6) |
| 2 | 7 | (2, 7) |

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📌 Instructions for Graphing:

1. On the top graph, plot the points from the first table and draw a line through them.
2. On the bottom graph, plot the points from the second table and draw a line through them.

These lines will represent the graphs of the two functions.

Let me know if you'd like a visual sketch or further explanation!