Worksheet for finding x- and y-intercepts of linear equations.

To find the x and y intercepts of each equation, we’ll use this simple rule:

- To find the x-intercept, set y = 0 and solve for x.
- To find the y-intercept, set x = 0 and solve for y.

Let’s go one by one.

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Problem 1: x + 5y = 10

→ x-intercept (set y=0):
x + 5(0) = 10 → x = 10
So, x-intercept is (10, 0)

→ y-intercept (set x=0):
0 + 5y = 10 → 5y = 10 → y = 2
So, y-intercept is (0, 2)

✔ Check: Plug back in — both work.

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Problem 2: 3x - 6y = 12

→ x-intercept (set y=0):
3x - 6(0) = 12 → 3x = 12 → x = 4
So, x-intercept is (4, 0)

→ y-intercept (set x=0):
3(0) - 6y = 12 → -6y = 12 → y = -2
So, y-intercept is (0, -2)

✔ Check: Both values satisfy the original equation.

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Problem 3: 4x + 7y = -4

→ x-intercept (set y=0):
4x + 7(0) = -4 → 4x = -4 → x = -1
So, x-intercept is (-1, 0)

→ y-intercept (set x=0):
4(0) + 7y = -4 → 7y = -4 → y = -4/7
So, y-intercept is (0, -4/7)

✔ Check: Correct fractions and signs.

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Problem 4: 2x + 4y = 18

→ x-intercept (set y=0):
2x + 4(0) = 18 → 2x = 18 → x = 9
So, x-intercept is (9, 0)

→ y-intercept (set x=0):
2(0) + 4y = 18 → 4y = 18 → y = 18/4 = 9/2 or 4.5
So, y-intercept is (0, 9/2) or (0, 4.5)

✔ Check: Simplified fraction correctly.

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Final Answer:
1. x-int: (10, 0), y-int: (0, 2)
2. x-int: (4, 0), y-int: (0, -2)
3. x-int: (-1, 0), y-int: (0, -4/7)
4. x-int: (9, 0), y-int: (0, 9/2)