Linear equations worksheet with function form conversion, table of values, and graphing grids.

Explanation:
We are given three linear equations and asked to write each in function form, which means solving for y in terms of x (i.e., y = …). Then, for the first two, we fill in a table by plugging in the given x-values to find y, and then write the coordinate pair (x, y). For the third, we only need function form and the table — no graphing required.

Let’s do each one step by step.

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Problem 5: 3x + y = 5

Step 1: Solve for y (function form):
Subtract 3x from both sides:
y = 5 − 3x
✔ Function Form: y = −3x + 5

Now fill the table:

| x | y = −3x + 5 | y | (x, y) |
|----|-------------|-----|------------|
| −2 | −3(−2)+5 = 6+5 = 11 | 11 | (−2, 11) |
| −1 | −3(−1)+5 = 3+5 = 8 | 8 | (−1, 8) |
| 0 | −3(0)+5 = 0+5 = 5 | 5 | (0, 5) |
| 1 | −3(1)+5 = −3+5 = 2 | 2 | (1, 2) |
| 2 | −3(2)+5 = −6+5 = −1 | −1 | (2, −1) |

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Problem 6: 4x + 4y = 8

Step 1: Solve for y.

First, simplify if possible. Divide entire equation by 4:
x + y = 2
Then subtract x:
y = 2 − x
✔ Function Form: y = −x + 2

Now fill the table:

| x | y = −x + 2 | y | (x, y) |
|----|------------|-----|------------|
| −2 | −(−2)+2 = 2+2 = 4 | 4 | (−2, 4) |
| −1 | −(−1)+2 = 1+2 = 3 | 3 | (−1, 3) |
| 0 | −0+2 = 2 | 2 | (0, 2) |
| 1 | −1+2 = 1 | 1 | (1, 1) |
| 2 | −2+2 = 0 | 0 | (2, 0) |

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Problem 7: 3x − 2y = 6

Step 1: Solve for y.

Start with:
3x − 2y = 6
Subtract 3x from both sides:
−2y = −3x + 6
Divide both sides by −2:
y = (−3x + 6) / (−2) = (3x − 6)/2 = (3/2)x − 3
✔ Function Form: y = (3/2)x − 3

Now fill the table using y = (3/2)x − 3:

| x | y = (3/2)x − 3 | y | (x, y) |
|----|----------------|-------------|---------------|
| −4 | (3/2)(−4) − 3 = −6 − 3 = −9 | −9 | (−4, −9) |
| −2 | (3/2)(−2) − 3 = −3 − 3 = −6 | −6 | (−2, −6) |
| 0 | (3/2)(0) − 3 = 0 − 3 = −3 | −3 | (0, −3) |
| 2 | (3/2)(2) − 3 = 3 − 3 = 0 | 0 | (2, 0) |
| 4 | (3/2)(4) − 3 = 6 − 3 = 3 | 3 | (4, 3) |

All calculations double-checked — correct.

Final Answer:
5) Function Form: y = −3x + 5
Table:
x = −2 → y = 11 → (−2, 11)
x = −1 → y = 8 → (−1, 8)
x = 0 → y = 5 → (0, 5)
x = 1 → y = 2 → (1, 2)
x = 2 → y = −1 → (2, −1)

6) Function Form: y = −x + 2
Table:
x = −2 → y = 4 → (−2, 4)
x = −1 → y = 3 → (−1, 3)
x = 0 → y = 2 → (0, 2)
x = 1 → y = 1 → (1, 1)
x = 2 → y = 0 → (2, 0)

7) Function Form: y = (3/2)x − 3
Table:
x = −4 → y = −9 → (−4, −9)
x = −2 → y = −6 → (−2, −6)
x = 0 → y = −3 → (0, −3)
x = 2 → y = 0 → (2, 0)
x = 4 → y = 3 → (4, 3)