Graphing Lines Worksheets - 15 Worksheets Library - Free Printable

Let’s solve each problem step by step.

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Problem 5: 3x + y = 5

We need to write this in function form, which means solving for y (so it looks like y = ...).

Start with:
> 3x + y = 5

Subtract 3x from both sides:
> y = -3x + 5

✔ Function Form: y = -3x + 5

Now fill in the table using x values: -2, -1, 0, 1, 2

- When x = -2 → y = -3(-2) + 5 = 6 + 5 = 11 → point: (-2, 11)
- When x = -1 → y = -3(-1) + 5 = 3 + 5 = 8 → point: (-1, 8)
- When x = 0 → y = -3(0) + 5 = 0 + 5 = 5 → point: (0, 5)
- When x = 1 → y = -3(1) + 5 = -3 + 5 = 2 → point: (1, 2)
- When x = 2 → y = -3(2) + 5 = -6 + 5 = -1 → point: (2, -1)

Table filled:

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

Graphing: Plot these points and draw a straight line through them. The line will go down steeply because slope is -3.

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Problem 6: 4x + 4y = 8

Write in function form → solve for y.

Start:
> 4x + 4y = 8

Subtract 4x from both sides:
> 4y = -4x + 8

Divide every term by 4:
> y = -x + 2

✔ Function Form: y = -x + 2

Fill table for x = -2, -1, 0, 1, 2

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

Table:

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

Graph: Plot points — they make a diagonal line going down gently (slope = -1).

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Problem 7: 3x - 2y = 6

Function form → solve for y.

Start:
> 3x - 2y = 6

Subtract 3x from both sides:
> -2y = -3x + 6

Divide every term by -2:
> y = (3/2)x - 3

✔ Function Form: y = (3/2)x - 3

Now find coordinates for x = -4, -2, 0, 2, 4

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

Table:

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

No graph needed per instructions.

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Final Answer:

Problem 5:
Function Form: y = -3x + 5
Table:
x | y = | y | (x, y)
--|------------|----|--------
-2| -3(-2)+5 | 11 | (-2, 11)
-1| -3(-1)+5 | 8 | (-1, 8)
0 | -3(0)+5 | 5 | (0, 5)
1 | -3(1)+5 | 2 | (1, 2)
2 | -3(2)+5 | -1 | (2, -1)

Problem 6:
Function Form: y = -x + 2
Table:
x | y = | y | (x, y)
--|-----------|----|--------
-2| -(-2)+2 | 4 | (-2, 4)
-1| -(-1)+2 | 3 | (-1, 3)
0 | -(0)+2 | 2 | (0, 2)
1 | -(1)+2 | 1 | (1, 1)
2 | -(2)+2 | 0 | (2, 0)

Problem 7:
Function Form: y = (3/2)x - 3
Table:
x | y = | y | (x, y)
--|------------------|----|--------
-4| (3/2)(-4)-3 | -9 | (-4, -9)
-2| (3/2)(-2)-3 | -6 | (-2, -6)
0 | (3/2)(0)-3 | -3 | (0, -3)
2 | (3/2)(2)-3 | 0 | (2, 0)
4 | (3/2)(4)-3 | 3 | (4, 3)