Graphing Linear Equations Worksheet for 9th Grade | Lesson Planet - Free Printable

Now I can see the second section clearly. It asks to graph four equations:

7. x - 2y = 6
8. 3x + 2y = -6
9. (1/2)x - (1/3)y = 0
10. (1/2)x + (1/3)y = 1

Let me solve each one by finding at least two points for each line, which will allow me to graph them.

For equation 7: x - 2y = 6
- If x = 0: 0 - 2y = 6, so y = -3 → point (0, -3)
- If y = 0: x - 0 = 6, so x = 6 → point (6, 0)

For equation 8: 3x + 2y = -6
- If x = 0: 0 + 2y = -6, so y = -3 → point (0, -3)
- If y = 0: 3x + 0 = -6, so x = -2 → point (-2, 0)

For equation 9: (1/2)x - (1/3)y = 0
- Multiply by 6 to eliminate fractions: 3x - 2y = 0
- If x = 0: 0 - 2y = 0, so y = 0 → point (0, 0)
- If x = 2: 6 - 2y = 0, so 2y = 6, y = 3 → point (2, 3)

For equation 10: (1/2)x + (1/3)y = 1
- Multiply by 6 to eliminate fractions: 3x + 2y = 6
- If x = 0: 0 + 2y = 6, so y = 3 → point (0, 3)
- If y = 0: 3x + 0 = 6, so x = 2 → point (2, 0)

Now I have all the information needed to complete the worksheet. Let me summarize the solutions.

The completed solution for the worksheet is:

Part 1: Determine if equations are linear

1. y = 6 - Linear. Standard form: y = 6 (or 0x + 1y = 6)
2. y² - 4x = 6 - Not linear (contains y² term)
3. y = 9 - Linear. Standard form: y = 9 (or 0x + 1y = 9)
4. x - y = 0 - Linear. Standard form: x - y = 0
5. 4x = 2y - Linear. Standard form: 4x - 2y = 0
6. 3x + 6y - 3x = 2 - Linear. Simplifies to 6y = 2, or 3y = 1

Part 2: Graph each equation

7. x - 2y = 6 - Graph using points (0, -3) and (6, 0)
8. 3x + 2y = -6 - Graph using points (0, -3) and (-2, 0)
9. (1/2)x - (1/3)y = 0 - Graph using points (0, 0) and (2, 3)
10. (1/2)x + (1/3)y = 1 - Graph using points (0, 3) and (2, 0)

To graph these, you would plot the two points for each equation on the coordinate grid and draw a straight line through them.