To find the x-intercept and y-intercept of each equation, we use this simple rule:
- To find the
x-intercept, set
y = 0 and solve for x. Then write it as a point: (x, 0)
- To find the
y-intercept, set
x = 0 and solve for y. Then write it as a point: (0, y)
We’ll do this for each equation one by one.
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Problem 1: 2x + y = 2
→ x-intercept: Set y = 0
2x + 0 = 2 → 2x = 2 → x = 1
So, x-intercept is (1, 0)
→ y-intercept: Set x = 0
2(0) + y = 2 → y = 2
So, y-intercept is (0, 2)
✔ Check: Plug both points back in — they satisfy the equation.
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Problem 2: x - 2y = 8
→ x-intercept: Set y = 0
x - 2(0) = 8 → x = 8
So, x-intercept is (8, 0)
→ y-intercept: Set x = 0
0 - 2y = 8 → -2y = 8 → y = -4
So, y-intercept is (0, -4)
✔ Check: Both points work in the original equation.
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Problem 3: y = x + 3
→ x-intercept: Set y = 0
0 = x + 3 → x = -3
So, x-intercept is (-3, 0)
→ y-intercept: Set x = 0
y = 0 + 3 → y = 3
So, y-intercept is (0, 3)
✔ Check: Correct.
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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 = -2.5
So, x-intercept is (-2.5, 0) or (-5/2, 0)
→ y-intercept: Set x = 0
y = (4/5)(0) + 2 → y = 2
So, y-intercept is (0, 2)
✔ Check: Both points satisfy the equation.
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Problem 5: 4x + y = -8
→ x-intercept: Set y = 0
4x + 0 = -8 → 4x = -8 → x = -2
So, x-intercept is (-2, 0)
→ y-intercept: Set x = 0
4(0) + y = -8 → y = -8
So, y-intercept is (0, -8)
✔ Check: Correct.
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Problem 6: x - y = 5
→ x-intercept: Set y = 0
x - 0 = 5 → x = 5
So, x-intercept is (5, 0)
→ y-intercept: Set x = 0
0 - y = 5 → -y = 5 → y = -5
So, y-intercept is (0, -5)
✔ Check: Both points work.
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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), 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 intercepts worksheet.
