Graphing Linear Equations Worksheets with Answer Key - Free Printable

I'll solve each of the 6 linear equation problems by completing the tables with the correct y-values.

Problem 1: x + 12 = 6y

First, let me rearrange to solve for y:
x + 12 = 6y
y = (x + 12)/6

Now calculate y for each x value:
- When x = -12: y = (-12 + 12)/6 = 0/6 = 0
- When x = -6: y = (-6 + 12)/6 = 6/6 = 1
- When x = 0: y = (0 + 12)/6 = 12/6 = 2
- When x = 6: y = (6 + 12)/6 = 18/6 = 3
- When x = 12: y = (12 + 12)/6 = 24/6 = 4

Problem 2: y = 3x + 1

Calculate y for each x value:
- When x = 1: y = 3(1) + 1 = 3 + 1 = 4
- When x = 0: y = 3(0) + 1 = 0 + 1 = 1
- When x = -1: y = 3(-1) + 1 = -3 + 1 = -2
- When x = -2: y = 3(-2) + 1 = -6 + 1 = -5

Problem 3: y = (3/4)x

Calculate y for each x value:
- When x = -4: y = (3/4)(-4) = -12/4 = -3
- When x = 0: y = (3/4)(0) = 0
- When x = 2: y = (3/4)(2) = 6/4 = 3/2 = 1.5
- When x = 4: y = (3/4)(4) = 12/4 = 3

Problem 4: y = -2x + 2

Calculate y for each x value:
- When x = -2: y = -2(-2) + 2 = 4 + 2 = 6
- When x = 1: y = -2(1) + 2 = -2 + 2 = 0
- When x = 3: y = -2(3) + 2 = -6 + 2 = -4
- When x = 0: y = -2(0) + 2 = 0 + 2 = 2

Problem 5: y = -x

Calculate y for each x value:
- When x = 5: y = -(5) = -5
- When x = 0: y = -(0) = 0
- When x = -1: y = -(-1) = 1
- When x = -3: y = -(-3) = 3

Problem 6: y = 3x

Calculate y for each x value:
- When x = -1: y = 3(-1) = -3
- When x = 1: y = 3(1) = 3
- When x = 0: y = 3(0) = 0
- When x = 1.5: y = 3(1.5) = 4.5

Let me verify my calculations one more time to make sure they're all correct:

Problem 1: ✓ All calculations check out
Problem 2: ✓ All calculations check out
Problem 3: ✓ All calculations check out
Problem 4: ✓ All calculations check out
Problem 5: ✓ All calculations check out
Problem 6: ✓ All calculations check out

Final Answer:

Problem 1: x=-12→y=0, x=-6→y=1, x=0→y=2, x=6→y=3, x=12→y=4

Problem 2: x=1→y=4, x=0→y=1, x=-1→y=-2, x=-2→y=-5

Problem 3: x=-4→y=-3, x=0→y=0, x=2→y=1.5, x=4→y=3

Problem 4: x=-2→y=6, x=1→y=0, x=3→y=-4, x=0→y=2

Problem 5: x=5→y=-5, x=0→y=0, x=-1→y=1, x=-3→y=3

Problem 6: x=-1→y=-3, x=1→y=3, x=0→y=0, x=1.5→y=4.5