Graphing Linear Equation Worksheets - Free Printable

Let’s solve each problem step by step. For each equation, we’ll:

1. Plug in the given x-values (or y-values if needed) to find the missing values.
2. Fill in the table.
3. (We won’t graph here since you didn’t ask for graphs — just the tables.)

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Problem 1: 7x – y = 7

Solve for y:
y = 7x – 7

Now plug in x = 0, 1, 2, 3, 4:

- x=0 → y = 7(0) – 7 = -7
- x=1 → y = 7(1) – 7 = 0
- x=2 → y = 14 – 7 = 7
- x=3 → y = 21 – 7 = 14
- x=4 → y = 28 – 7 = 21

Table:
x | 0 | 1 | 2 | 3 | 4
y | -7| 0 | 7 |14 |21

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Problem 2: 2x – 8 = 6y

Solve for y:
Divide both sides by 6:
y = (2x – 8)/6 = (x – 4)/3

Plug in x = -8, -6, -4, -2, 0:

- x=-8 → y = (-8–4)/3 = -12/3 = -4
- x=-6 → y = (-6–4)/3 = -10/3 ≈ -3.33? Wait — let’s check original equation.

Wait — maybe better to use original: 2x – 8 = 6y → so y = (2x – 8)/6

But let’s compute exactly:

x=-8: 2*(-8) – 8 = -16 – 8 = -24 → y = -24/6 = -4 ✔
x=-6: 2*(-6) – 8 = -12 – 8 = -20 → y = -20/6 = -10/3 → not integer? But table expects integers? Let me double-check.

Wait — maybe I made a mistake. Let’s re-solve:

Original: 2x – 8 = 6y → divide both sides by 2: x – 4 = 3y → so y = (x – 4)/3

So:

x=-8 → y = (-8–4)/3 = -12/3 = -4
x=-6 → y = (-6–4)/3 = -10/3 → still fraction. Hmm.

But looking at the table, it has x from -8 to 0, and likely expects integer y. Maybe I misread the equation?

Wait — perhaps it’s 2x – 8y = 6? No, image says “2x – 8 = 6y”

Actually, let’s accept fractions if needed — but let’s see what the problem expects.

Alternatively, maybe solve for x? No, table gives x, asks for y.

Let’s proceed with exact values:

x=-8 → y = (2*(-8)-8)/6 = (-16-8)/6 = -24/6 = -4
x=-6 → (2*(-6)-8)/6 = (-12-8)/6 = -20/6 = -10/3 → write as -3.33? But probably they want fractions or maybe I have error.

Wait — let me check problem 2 again. The image shows:

“2) 2x – 8 = 6y” and x values: -8, -6, -4, -2, 0

Let me calculate all:

x=-8: 2*(-8) = -16; -16 -8 = -24; -24 / 6 = -4 → y=-4
x=-6: 2*(-6)= -12; -12-8= -20; -20/6 = -10/3 → not nice.

Perhaps it's 2x - 8y = 6? But no, the image clearly says "2x – 8 = 6y"

Maybe typo in my reading? Let me assume it's correct and proceed with fractions.

But wait — let’s look at problem 3: y = 12 - 2x — that’s easy.

Perhaps for problem 2, we can leave as fractions or simplify.

But let’s do exact:

x=-8 → y = -4
x=-6 → y = -20/6 = -10/3
x=-4 → 2*(-4)-8 = -8-8= -16; -16/6 = -8/3
x=-2 → 2*(-2)-8 = -4-8= -12; -12/6 = -2
x=0 → 0-8= -8; -8/6 = -4/3

This seems messy. Perhaps the equation is different? Or maybe I should solve for x instead? No, table has x given.

Another thought: maybe it's 2x - 8 = 6y, but perhaps they want us to rearrange differently.

Or perhaps it's 2(x - 8) = 6y? But no, it's written as 2x – 8 = 6y.

I think we have to go with the math.

But let’s check online or standard problems — actually, in many worksheets, this might be a typo, but since we must solve as given, let's proceed.

However, looking back at the user's image description, it's possible that for problem 2, the equation is meant to be solved with integer outputs, so perhaps I miscalculated.

Let me try solving for y in terms of x:

From 2x - 8 = 6y, then y = (2x - 8)/6 = (x - 4)/3

So for x to give integer y, x-4 must be divisible by 3.

x=-8: -8-4= -12, divisible by 3 → y=-4
x=-6: -6-4= -10, not divisible by 3 → y=-10/3
x=-4: -4-4= -8, not divisible → y=-8/3
x=-2: -2-4= -6, divisible → y=-2
x=0: 0-4= -4, not divisible → y=-4/3

So only some are integers. But the table has blanks for y, so we fill with fractions.

But perhaps in the context, they expect decimal or fraction. Let's keep as fractions.

To make it neat, let's write as simplified fractions.

So for problem 2:

x | -8 | -6 | -4 | -2 | 0
y | -4 | -10/3 | -8/3 | -2 | -4/3

But this seems odd for a worksheet. Perhaps the equation is 2x - 8y = 6? Let me verify with the image description.

The user wrote: "2) 2x – 8 = 6y" — so I think we have to go with that.

Maybe it's 2x - 8 = 6y, and they want us to use the values as is.

Let's move on and come back.

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Problem 3: y = 12 - 2x

Easy. Plug in x = -12, -6, 0, 6, 12

x=-12: y=12 -2*(-12)=12+24=36
x=-6: y=12 -2*(-6)=12+12=24
x=0: y=12 -0=12
x=6: y=12-12=0
x=12: y=12-24= -12

Table:
x | -12 | -6 | 0 | 6 | 12
y | 36 | 24 | 12| 0 | -12

Good.

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Problem 4: 15 = 10x + 5y

Solve for y.

15 = 10x + 5y
Subtract 10x: 15 - 10x = 5y
Divide by 5: y = 3 - 2x

Now plug in x = -2, -1, 0, 2, 3

x=-2: y=3 -2*(-2)=3+4=7
x=-1: y=3 -2*(-1)=3+2=5
x=0: y=3 -0=3
x=2: y=3 -4= -1
x=3: y=3 -6= -3

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

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Problem 5: 6y = -x + 12

Solve for y: y = (-x + 12)/6

Plug in x = -8, -4, 0, 4, 8

x=-8: y = (-(-8) +12)/6 = (8+12)/6 = 20/6 = 10/3 ≈3.33
x=-4: y = (4 +12)/6 = 16/6 = 8/3
x=0: y=12/6=2
x=4: y=(-4+12)/6=8/6=4/3
x=8: y=(-8+12)/6=4/6=2/3

Again fractions. But let's write as simplified fractions.

Table:
x | -8 | -4 | 0 | 4 | 8
y | 10/3 | 8/3 | 2 | 4/3 | 2/3

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Problem 6: x + 12 = 6y

Solve for y: y = (x + 12)/6

Plug in x = -12, -6, 0, 6, 12

x=-12: y=( -12 +12)/6=0/6=0
x=-6: y=( -6+12)/6=6/6=1
x=0: y=12/6=2
x=6: y=18/6=3
x=12: y=24/6=4

Nice! Integers.

Table:
x | -12 | -6 | 0 | 6 | 12
y | 0 | 1 | 2 | 3 | 4

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Problem 7: -x + 9y = 9

Solve for y.

9y = x + 9
y = (x + 9)/9

Given x = 9, 18, 27, 36, 45

x=9: y=(9+9)/9=18/9=2
x=18: y=(18+9)/9=27/9=3
x=27: y=36/9=4
x=36: y=45/9=5
x=45: y=54/9=6

Table:
x | 9 | 18 | 27 | 36 | 45
y | 2 | 3 | 4 | 5 | 6

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Problem 8: -25 = 5y - x

Solve for y.

-25 = 5y - x
Add x to both sides: x - 25 = 5y
Divide by 5: y = (x - 25)/5

Given x = 5, 10, 15, 20, 25

x=5: y=(5-25)/5= -20/5= -4
x=10: y=(10-25)/5= -15/5= -3
x=15: y=(15-25)/5= -10/5= -2
x=20: y=(20-25)/5= -5/5= -1
x=25: y=(25-25)/5=0/5=0

Table:
x | 5 | 10 | 15 | 20 | 25
y | -4| -3 | -2 | -1 | 0

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Problem 9: 2y = -x + 8

Solve for y: y = (-x + 8)/2

Given x = -2, 0, 2, 4, 6

x=-2: y= -(-2) +8 /2 = (2+8)/2=10/2=5
x=0: y=(0+8)/2=8/2=4
x=2: y=(-2+8)/2=6/2=3
x=4: y=(-4+8)/2=4/2=2
x=6: y=(-6+8)/2=2/2=1

Table:
x | -2 | 0 | 2 | 4 | 6
y | 5 | 4 | 3 | 2 | 1

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Now, going back to Problem 2 and 5 which had fractions. In many school worksheets, they might expect fractions or decimals, but since the other problems have integers, perhaps there's a mistake in my interpretation.

For Problem 2: "2x – 8 = 6y"

Perhaps it's 2x - 8y = 6? Let me try that.

If 2x - 8y = 6, then solve for y.

2x - 6 = 8y → y = (2x - 6)/8 = (x - 3)/4

Then for x=-8: y=(-8-3)/4= -11/4 — worse.

Or if it's 2(x - 8) = 6y, then 2x - 16 = 6y, y=(2x-16)/6=(x-8)/3

x=-8: y=(-8-8)/3= -16/3 — no.

Perhaps the equation is 2x - 8 = 6y, and we have to live with fractions.

But let's look at the x-values: -8,-6,-4,-2,0

For y to be integer, from y=(x-4)/3, x-4 must be divisible by 3.

x=-8: -12/3=-4 ok
x=-6: -10/3 not
x=-4: -8/3 not
x=-2: -6/3=-2 ok
x=0: -4/3 not

So only two are integers. Perhaps in the worksheet, they allow fractions, or maybe I need to round, but that doesn't make sense.

Another idea: perhaps the equation is 2x - 8 = 6y, but they want us to solve for x? No, table has x given.

I think for accuracy, I'll provide the fractional answers.

Similarly for Problem 5.

But let's double-check Problem 5: "6y = -x + 12"

With x=-8,-4,0,4,8

As calculated: y=10/3, 8/3, 2, 4/3, 2/3

Perhaps write as mixed numbers, but fractions are fine.

Now, for the final answer, since the user asked to solve the problem, and the problem is to complete the tables, I will provide all tables filled.

Also, for Problem 2, let's write the y-values as fractions.

So summarizing all:

Final Answer:

Here are the completed tables for each problem:

1) 7x – y = 7
x | 0 | 1 | 2 | 3 | 4
y | -7| 0 | 7 |14 |21

2) 2x – 8 = 6y
x | -8 | -6 | -4 | -2 | 0
y | -4 | -10/3 | -8/3 | -2 | -4/3

3) y = 12 - 2x
x | -12 | -6 | 0 | 6 | 12
y | 36 | 24 | 12| 0 | -12

4) 15 = 10x + 5y
x | -2 | -1 | 0 | 2 | 3
y | 7 | 5 | 3 | -1| -3

5) 6y = -x + 12
x | -8 | -4 | 0 | 4 | 8
y | 10/3 | 8/3 | 2 | 4/3 | 2/3

6) x + 12 = 6y
x | -12 | -6 | 0 | 6 | 12
y | 0 | 1 | 2 | 3 | 4

7) -x + 9y = 9
x | 9 | 18 | 27 | 36 | 45
y | 2 | 3 | 4 | 5 | 6

8) -25 = 5y - x
x | 5 | 10 | 15 | 20 | 25
y | -4| -3 | -2 | -1 | 0

9) 2y = -x + 8
x | -2 | 0 | 2 | 4 | 6
y | 5 | 4 | 3 | 2 | 1

Note: For problems 2 and 5, the y-values are fractions because the equations result in non-integer outputs for those x-values. If your teacher expects decimals, you can convert them, but fractions are exact.

Since the instruction was to solve the problem accurately, and these are the correct mathematical solutions, this is the answer.