FREE Eighth Grade Graphing Linear Equations Worksheet - Free Printable

To graph each linear equation, we’ll use the slope-intercept form:
y = mx + b, where:
- m is the slope (rise over run)
- b is the y-intercept (where the line crosses the y-axis)

We’ll go through each equation one by one. For each, we’ll find two points and draw a straight line through them.

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1. y = (1/2)x + 1

→ Slope = 1/2 → rise 1, run 2
→ Y-intercept = 1 → point (0, 1)
From (0,1), go up 1, right 2 → (2, 2)
Plot (0,1) and (2,2), draw line.

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2. y = 3x - 2

→ Slope = 3 → rise 3, run 1
→ Y-intercept = -2 → point (0, -2)
From (0,-2), go up 3, right 1 → (1, 1)
Plot (0,-2) and (1,1), draw line.

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3. y = (1/5)x - 4

→ Slope = 1/5 → rise 1, run 5
→ Y-intercept = -4 → point (0, -4)
From (0,-4), go up 1, right 5 → (5, -3)
Plot (0,-4) and (5,-3), draw line.

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4. y = 6x - 4

→ Slope = 6 → rise 6, run 1
→ Y-intercept = -4 → point (0, -4)
From (0,-4), go up 6, right 1 → (1, 2)
Plot (0,-4) and (1,2), draw line.

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5. y = 2x + 3

→ Slope = 2 → rise 2, run 1
→ Y-intercept = 3 → point (0, 3)
From (0,3), go up 2, right 1 → (1, 5)
Plot (0,3) and (1,5), draw line.

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6. x = -2

→ This is a vertical line at x = -2
→ Draw a straight vertical line crossing x = -2 on the x-axis.
→ It goes through all y-values when x = -2.

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7. 8x + y = 0

Rewrite in slope-intercept form:
→ y = -8x
→ Slope = -8 → fall 8, run 1
→ Y-intercept = 0 → point (0, 0)
From (0,0), go down 8, right 1 → (1, -8) — but that’s off most grids.
Better: From (0,0), go down 4, right 0.5? Not ideal.
Use smaller steps: Since slope = -8, from (0,0), go down 8, right 1 → too far.
Alternative: Use x = 1 → y = -8 → still far.
Wait — maybe pick x = 0.5 → y = -4 → still not great for grid.
Actually, let’s use:
At x = 0 → y = 0 → (0,0)
At x = 1 → y = -8 → too low.
But if grid only goes to ±5 or so, better to scale:
Slope = -8 means very steep downward.
From (0,0), go down 8 units for every 1 right — but if grid is small, just show direction.
Alternatively, rewrite as:
When x = 1, y = -8 → too big.
Try x = 0.5 → y = -4 → still maybe too big.
Actually, perhaps the grid allows it? If not, use:
Point A: (0, 0)
Point B: (-1, 8) ← because if x = -1, y = -8*(-1) = 8 → yes!
So plot (0,0) and (-1,8). That works if grid goes to y=8.
If grid is limited, adjust accordingly — but mathematically correct.

Assuming standard grid with range -5 to 5, this might be tricky. But since problem says “graph”, we assume you can extend or use appropriate scale.

Actually, let’s check: Maybe I made mistake?
Equation: 8x + y = 0 → y = -8x
Yes. So if x = 1, y = -8; x = -1, y = 8.
So if your grid has y from -10 to 10, fine. Otherwise, note it's very steep.

For school purposes, often they accept plotting (0,0) and another point even if off-grid, or use fractional steps.

But let’s proceed with (0,0) and (-1,8) if possible.

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8. 3x + 4y = 12

Convert to slope-intercept:
4y = -3x + 12
y = (-3/4)x + 3
→ Slope = -3/4 → fall 3, run 4
→ Y-intercept = 3 → (0, 3)
From (0,3), go down 3, right 4 → (4, 0)
Perfect! Plot (0,3) and (4,0), draw line.

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9. 4x - 10y = 20

Convert:
-10y = -4x + 20
Divide both sides by -10:
y = (4/10)x - 2 → simplify: y = (2/5)x - 2
→ Slope = 2/5 → rise 2, run 5
→ Y-intercept = -2 → (0, -2)
From (0,-2), go up 2, right 5 → (5, 0)
Plot (0,-2) and (5,0), draw line.

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10. y = (1/2)x + 1

Same as #1!
→ Already did: (0,1) and (2,2)

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11. y = 3x - 1

→ Slope = 3 → rise 3, run 1
→ Y-intercept = -1 → (0, -1)
From (0,-1), go up 3, right 1 → (1, 2)
Plot (0,-1) and (1,2), draw line.

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12. -2x + 8y = 16

Convert:
8y = 2x + 16
Divide by 8:
y = (2/8)x + 2 → simplify: y = (1/4)x + 2
→ Slope = 1/4 → rise 1, run 4
→ Y-intercept = 2 → (0, 2)
From (0,2), go up 1, right 4 → (4, 3)
Plot (0,2) and (4,3), draw line.

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13. x + y = 2

Convert:
y = -x + 2
→ Slope = -1 → fall 1, run 1
→ Y-intercept = 2 → (0, 2)
From (0,2), go down 1, right 1 → (1, 1)
Also, x-intercept: set y=0 → x=2 → (2,0)
Plot (0,2) and (2,0), draw line.

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Now, double-checking calculations:

All conversions look correct.

For #7: 8x + y = 0 → y = -8x → correct. Points (0,0) and (-1,8) are valid.

For #9: 4x -10y =20 → y=(2/5)x -2 → correct.

For #12: -2x+8y=16 → y=(1/4)x +2 → correct.

No arithmetic errors found.

Final Answer:
Graph each equation using the points derived above. Each line should be drawn accurately based on its slope and y-intercept (or intercepts for vertical lines).