Let’s solve each problem one by one. For each equation, we’ll find the x-intercept and y-intercept as points.
Remember:
- To find the
x-intercept, set
y = 0 and solve for x. The point will be (x, 0).
- To find the
y-intercept, set
x = 0 and solve for y. The point will be (0, y).
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Problem 1: 2x + y = 2
→ x-intercept: Set y = 0
2x + 0 = 2 → 2x = 2 → x = 1 → Point:
(1, 0)
→ y-intercept: Set x = 0
2(0) + y = 2 → y = 2 → Point:
(0, 2)
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Problem 2: x - 2y = 8
→ x-intercept: Set y = 0
x - 2(0) = 8 → x = 8 → Point:
(8, 0)
→ y-intercept: Set x = 0
0 - 2y = 8 → -2y = 8 → y = -4 → Point:
(0, -4)
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Problem 3: y = x + 3
→ x-intercept: Set y = 0
0 = x + 3 → x = -3 → Point:
(-3, 0)
→ y-intercept: Set x = 0
y = 0 + 3 → y = 3 → Point:
(0, 3)
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Problem 4: y = (4/5)x + 2
→ x-intercept: Set y = 0
0 = (4/5)x + 2 → Subtract 2: -2 = (4/5)x
Multiply both sides by 5: -10 = 4x → Divide by 4: x = -10/4 = -5/2 → Point:
(-5/2, 0) or
(-2.5, 0)
→ y-intercept: Set x = 0
y = (4/5)(0) + 2 → y = 2 → Point:
(0, 2)
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Problem 5: 4x + y = -8
→ x-intercept: Set y = 0
4x + 0 = -8 → 4x = -8 → x = -2 → Point:
(-2, 0)
→ y-intercept: Set x = 0
4(0) + y = -8 → y = -8 → Point:
(0, -8)
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Problem 6: x - y = 5
→ x-intercept: Set y = 0
x - 0 = 5 → x = 5 → Point:
(5, 0)
→ y-intercept: Set x = 0
0 - y = 5 → -y = 5 → y = -5 → Point:
(0, -5)
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Final Answer:
1. x-intercept: (1, 0), y-intercept: (0, 2)
2. x-intercept: (8, 0), y-intercept: (0, -4)
3. x-intercept: (-3, 0), y-intercept: (0, 3)
4. x-intercept: (-5/2, 0) or (-2.5, 0), y-intercept: (0, 2)
5. x-intercept: (-2, 0), y-intercept: (0, -8)
6. x-intercept: (5, 0), y-intercept: (0, -5)
Parent Tip: Review the logic above to help your child master the concept of find slope and y intercept from equation worksheet.
