1) x + 2y = 6
- Find intercepts:
- x-intercept: Set y=0 → x = 6 → (6, 0)
- y-intercept: Set x=0 → 2y = 6 → y = 3 → (0, 3)
- Plot points (6, 0) and (0, 3), draw line.
2) 3x + 2y = -8
- Find intercepts:
- x-intercept: Set y=0 → 3x = -8 → x = -8/3 ≈ -2.67 → (-8/3, 0)
- y-intercept: Set x=0 → 2y = -8 → y = -4 → (0, -4)
- Plot points (-8/3, 0) and (0, -4), draw line.
3) x - 3y = 0
- This is a proportional relationship.
- Solve for y: y = (1/3)x
- Passes through origin (0, 0).
- Pick another point: Let x=3 → y=1 → (3, 1)
- Plot (0, 0) and (3, 1), draw line.
4) x + 5y = 25
- Find intercepts:
- x-intercept: Set y=0 → x = 25 → (25, 0) — outside grid
- y-intercept: Set x=0 → 5y = 25 → y = 5 → (0, 5)
- Use another point: Let y=4 → x + 20 = 25 → x = 5 → (5, 4)
- Plot (0, 5) and (5, 4), draw line.
5) 4x - y = 3
- Solve for y: y = 4x - 3
- y-intercept: (0, -3)
- Another point: Let x=1 → y = 4(1) - 3 = 1 → (1, 1)
- Plot (0, -3) and (1, 1), draw line.
6) 3x + 2y = 8
- Find intercepts:
- x-intercept: Set y=0 → 3x = 8 → x = 8/3 ≈ 2.67 → (8/3, 0)
- y-intercept: Set x=0 → 2y = 8 → y = 4 → (0, 4)
- Plot points (8/3, 0) and (0, 4), draw line.
Parent Tip: Review the logic above to help your child master the concept of graphing lines in standard form worksheet.
