Practice worksheet for finding x and y intercepts of linear equations.

Let's solve each problem step by step to find the x-intercept and y-intercept of each linear equation.

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🔍 How to Find Intercepts:

- X-intercept: Set $ y = 0 $, then solve for $ x $. The point is $ (x, 0) $
- Y-intercept: Set $ x = 0 $, then solve for $ y $. The point is $ (0, y) $

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✔ Problem 1: $ 3x + 6y = 18 $

#### X-intercept (set $ y = 0 $):
$$
3x + 6(0) = 18 \Rightarrow 3x = 18 \Rightarrow x = 6
$$
So, x-int: $ (6, 0) $

#### Y-intercept (set $ x = 0 $):
$$
3(0) + 6y = 18 \Rightarrow 6y = 18 \Rightarrow y = 3
$$
So, y-int: $ (0, 3) $

✔ Answer:
x-int: $ (6, 0) $, y-int: $ (0, 3) $

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✔ Problem 2: $ 4x + y = -8 $

#### X-intercept ($ y = 0 $):
$$
4x + 0 = -8 \Rightarrow 4x = -8 \Rightarrow x = -2
$$
So, x-int: $ (-2, 0) $

#### Y-intercept ($ x = 0 $):
$$
4(0) + y = -8 \Rightarrow y = -8
$$
So, y-int: $ (0, -8) $

✔ Answer:
x-int: $ (-2, 0) $, y-int: $ (0, -8) $

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✔ Problem 3: $ 7x - 3y = -21 $

#### X-intercept ($ y = 0 $):
$$
7x - 3(0) = -21 \Rightarrow 7x = -21 \Rightarrow x = -3
$$
So, x-int: $ (-3, 0) $

#### Y-intercept ($ x = 0 $):
$$
7(0) - 3y = -21 \Rightarrow -3y = -21 \Rightarrow y = 7
$$
So, y-int: $ (0, 7) $

✔ Answer:
x-int: $ (-3, 0) $, y-int: $ (0, 7) $

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✔ Problem 4: $ x - 9y = -45 $

#### X-intercept ($ y = 0 $):
$$
x - 9(0) = -45 \Rightarrow x = -45
$$
So, x-int: $ (-45, 0) $

#### Y-intercept ($ x = 0 $):
$$
0 - 9y = -45 \Rightarrow -9y = -45 \Rightarrow y = 5
$$
So, y-int: $ (0, 5) $

✔ Answer:
x-int: $ (-45, 0) $, y-int: $ (0, 5) $

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✔ Problem 5: $ 2x + 6y = -24 $

#### X-intercept ($ y = 0 $):
$$
2x + 6(0) = -24 \Rightarrow 2x = -24 \Rightarrow x = -12
$$
So, x-int: $ (-12, 0) $

#### Y-intercept ($ x = 0 $):
$$
2(0) + 6y = -24 \Rightarrow 6y = -24 \Rightarrow y = -4
$$
So, y-int: $ (0, -4) $

✔ Answer:
x-int: $ (-12, 0) $, y-int: $ (0, -4) $

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✔ Problem 6: $ 5x + 3y = -15 $

#### X-intercept ($ y = 0 $):
$$
5x + 3(0) = -15 \Rightarrow 5x = -15 \Rightarrow x = -3
$$
So, x-int: $ (-3, 0) $

#### Y-intercept ($ x = 0 $):
$$
5(0) + 3y = -15 \Rightarrow 3y = -15 \Rightarrow y = -5
$$
So, y-int: $ (0, -5) $

✔ Answer:
x-int: $ (-3, 0) $, y-int: $ (0, -5) $

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📝 Final Answers Summary:

| Problem | x-int | y-int |
|--------|-------------|--------------|
| 1 | (6, 0) | (0, 3) |
| 2 | (-2, 0) | (0, -8) |
| 3 | (-3, 0) | (0, 7) |
| 4 | (-45, 0) | (0, 5) |
| 5 | (-12, 0) | (0, -4) |
| 6 | (-3, 0) | (0, -5) |

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✔ Tip: Always remember:
- To find x-intercept, plug in $ y = 0 $
- To find y-intercept, plug in $ x = 0 $
- Then solve the resulting equation.

Let me know if you'd like this formatted as a printable worksheet!