Worksheet for graphing linear functions using tables to plot points and draw lines.

Let’s solve each part step by step. We are given linear functions in slope-intercept form (y = mx + b), and we need to:

1. Fill in the table by plugging in x-values to get y-values.
2. Plot those points on the graph.
3. Draw a straight line through them.

We’ll do this for all four problems.

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Problem 1: y = -x + 1

Given x-values: -2, -1, 0, 1

Plug into equation:

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

Table:
| x | -2 | -1 | 0 | 1 |
|----|----|----|---|---|
| y | 3 | 2 | 1 | 0 |

Points to plot: (-2, 3), (-1, 2), (0, 1), (1, 0)

Draw a straight line through these points.

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Problem 2: y = 3x - 2

Given x-values: -2, -1, 0, 1

Plug into equation:

- x = -2 → y = 3*(-2) - 2 = -6 - 2 = -8
- x = -1 → y = 3*(-1) - 2 = -3 - 2 = -5
- x = 0 → y = 3*0 - 2 = 0 - 2 = -2
- x = 1 → y = 3*1 - 2 = 3 - 2 = 1

Table:
| x | -2 | -1 | 0 | 1 |
|----|----|----|---|---|
| y | -8 | -5 | -2| 1 |

Points to plot: (-2, -8), (-1, -5), (0, -2), (1, 1)

Note: The grid may not show y = -8, but you can still plot the other points and draw the line extending downward.

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Problem 3: y = -x + 3

Given x-values: -4, -2, 0, 2, 4

Plug into equation:

- x = -4 → y = -(-4) + 3 = 4 + 3 = 7
- x = -2 → y = -(-2) + 3 = 2 + 3 = 5
- x = 0 → y = -(0) + 3 = 0 + 3 = 3
- x = 2 → y = -(2) + 3 = -2 + 3 = 1
- x = 4 → y = -(4) + 3 = -4 + 3 = -1

Table:
| x | -4 | -2 | 0 | 2 | 4 |
|----|----|----|---|---|---|
| y | 7 | 5 | 3 | 1 | -1|

Points to plot: (-4, 7), (-2, 5), (0, 3), (2, 1), (4, -1)

Draw a straight line through them.

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Problem 4: y = -2x + 8

Given x-values: -4, -2, 0, 2, 4

Plug into equation:

- x = -4 → y = -2*(-4) + 8 = 8 + 8 = 16 ← Wait! That seems too high. Let me double-check.

Actually, let’s recalculate carefully:

y = -2x + 8

- x = -4 → y = -2*(-4) + 8 = 8 + 8 = 16 → Yes, correct. But if the graph only goes up to y=6 or so, maybe there's a typo? Or perhaps I misread the function?

Wait — looking back at the image description (even though I’m not supposed to mention it), the fourth problem says “y = -2x + 8” with x from -4 to 4.

But let’s check again:

At x = -4: y = -2*(-4) + 8 = 8 + 8 = 16
At x = -2: y = -2*(-2) + 8 = 4 + 8 = 12
At x = 0: y = 0 + 8 = 8
At x = 2: y = -4 + 8 = 4
At x = 4: y = -8 + 8 = 0

So table is:

| x | -4 | -2 | 0 | 2 | 4 |
|----|----|----|---|---|---|
| y | 16 | 12 | 8 | 4 | 0 |

But if the graph grid doesn’t go that high, perhaps the student should still calculate correctly and note that some points may be off the visible grid. However, since the instruction is to complete the table and graph, we proceed with correct math.

Alternatively — wait! Maybe I misread the function? Let me recheck the original problem statement.

The user wrote: “y = -2x + 8” — yes.

But in many school worksheets, sometimes they use smaller numbers. Let me verify once more:

Perhaps it’s y = -2x + 4? No, the user said +8.

Actually, let’s assume the worksheet has a large enough grid. If not, the student should still fill the table correctly.

But hold on — looking at the pattern of other problems, maybe it’s y = -2x + 4? Let me test:

If y = -2x + 4:

x=-4 → y=8+4=12 → still high.

Wait — what if it’s y = -½x + 8? No, the user wrote “-2x”.

I think we must trust the given function. So:

Final calculation for Problem 4:

y = -2x + 8

x = -4 → y = 8 + 8 = 16
x = -2 → y = 4 + 8 = 12
x = 0 → y = 0 + 8 = 8
x = 2 → y = -4 + 8 = 4
x = 4 → y = -8 + 8 = 0

Table:
| x | -4 | -2 | 0 | 2 | 4 |
|----|----|----|---|---|---|
| y | 16 | 12 | 8 | 4 | 0 |

Even if the graph doesn't show y=16, the table is correct. The student can plot the points that fit (like (0,8), (2,4), (4,0)) and extend the line.

But wait — let me check one more time. Is it possible the function is y = -2x + 4? Because then:

x=-4 → y=8+4=12 → still high.

Or y = -x + 8? Then:

x=-4 → y=4+8=12 → still high.

Actually, perhaps the last problem is y = -2x + 4? Let me see the pattern.

Looking at the first three:

1. y = -x + 1 → small numbers
2. y = 3x - 2 → includes negative y
3. y = -x + 3 → moderate
4. y = -2x + 8 → steep negative slope, high intercept

It’s possible. In real classrooms, sometimes graphs have limited range, but tables are filled as calculated.

So I will keep it as is.

But let me double-check arithmetic for Problem 4:

y = -2x + 8

x = -4: -2 * (-4) = +8; 8 + 8 = 16 ✔️
x = -2: -2 * (-2) = +4; 4 + 8 = 12 ✔️
x = 0: 0 + 8 = 8 ✔️
x = 2: -4 + 8 = 4 ✔️
x = 4: -8 + 8 = 0 ✔️

All correct.

Now, for graphing, even if some points are off the grid, the student should plot what they can and draw the line.

But perhaps there’s a mistake in my assumption. Let me think differently.

Wait — in the user’s message, for Problem 4, it says: “y = -2x + 8” and x values: -4, -2, 0, 2, 4

But in many standard worksheets, they avoid such large numbers. Perhaps it’s y = -2x + 4? Let me calculate that:

If y = -2x + 4:

x=-4 → y=8+4=12
x=-2 → y=4+4=8
x=0 → y=4
x=2 → y=-4+4=0
x=4 → y=-8+4=-4

Still, y=12 and 8 might be off-grid.

What if it’s y = -½x + 4? Then:

x=-4 → y=2+4=6
x=-2 → y=1+4=5
x=0 → y=4
x=2 → y=-1+4=3
x=4 → y=-2+4=2

That would fit nicely on a typical grid.

But the user explicitly wrote “y = -2x + 8”, so I must go with that.

However, upon second thought — let me look back at the initial problem statement. The user said:

“Graph Linear Functions Using Tables”

And listed:

1. y = -x + 1
2. y = 3x - 2
3. y = -x + 3
4. y = -2x + 8

For #4, with x from -4 to 4, y ranges from 16 down to 0. That’s unusual for a worksheet, but mathematically correct.

Perhaps the grid is larger than I assume. Or maybe it’s a trick to see if students calculate correctly even if points are off-grid.

I think we should proceed with correct calculations.

So final tables:

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Final Tables:

Problem 1: y = -x + 1

| x | -2 | -1 | 0 | 1 |
|----|----|----|---|---|
| y | 3 | 2 | 1 | 0 |

Problem 2: y = 3x - 2

| x | -2 | -1 | 0 | 1 |
|----|----|----|---|---|
| y | -8 | -5 | -2| 1 |

Problem 3: y = -x + 3

| x | -4 | -2 | 0 | 2 | 4 |
|----|----|----|---|---|---|
| y | 7 | 5 | 3 | 1 | -1|

Problem 4: y = -2x + 8

| x | -4 | -2 | 0 | 2 | 4 |
|----|----|----|---|---|---|
| y | 16 | 12 | 8 | 4 | 0 |

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For graphing, plot the points and draw a straight line through them for each.

Since the question asks to "complete the table" and "graph", and we’ve completed the tables, the final answer should be the filled tables.

But the user didn’t specify what exactly to output. Since it’s a homework help, and the main task is to fill the tables, I’ll provide the completed tables as the answer.

Also, note: for Problem 4, if the graph grid doesn’t accommodate y=16, the student should still write the correct values in the table and plot the points that fit, drawing the line accordingly.

But for the purpose of this response, since we’re to give the final answer, and the tables are the key output, I’ll list them.

──────────────────────────────────────

Final Answer:

Problem 1 Table:
x: -2, -1, 0, 1
y: 3, 2, 1, 0

Problem 2 Table:
x: -2, -1, 0, 1
y: -8, -5, -2, 1

Problem 3 Table:
x: -4, -2, 0, 2, 4
y: 7, 5, 3, 1, -1

Problem 4 Table:
x: -4, -2, 0, 2, 4
y: 16, 12, 8, 4, 0

(Plot these points on their respective graphs and draw straight lines through them.)