Standard Form Linear Equation Worksheet - Fill Online, Printable ... - Free Printable

You're working on Unit 3: Lesson 8 – Standard Form, where you need to find the x-intercept and y-intercept of each linear equation (in standard form: Ax + By = C), and then graph the line using those two points.

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🔑 Key Concept:

- The x-intercept is where the line crosses the x-axis → y = 0
- The y-intercept is where the line crosses the y-axis → x = 0

So for any equation in standard form, plug in y=0 to find x-intercept, and x=0 to find y-intercept.

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Let’s solve each one step by step:

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✔ 1) x + 2y = 8

x-intercept (set y = 0):
x + 2(0) = 8 → x = 8
→ x-int = (8, 0)

y-intercept (set x = 0):
0 + 2y = 8 → y = 4
→ y-int = (0, 4)

✔ Fill in:
x-int = 8
y-int = 4

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✔ 2) 3x - y = 9

x-intercept (set y = 0):
3x - 0 = 9 → 3x = 9 → x = 3
→ x-int = (3, 0)

y-intercept (set x = 0):
0 - y = 9 → -y = 9 → y = -9
→ y-int = (0, -9)

✔ Fill in:
x-int = 3
y-int = -9

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✔ 3) -5x + 6y = 30

x-intercept (set y = 0):
-5x + 0 = 30 → -5x = 30 → x = -6
→ x-int = (-6, 0)

y-intercept (set x = 0):
0 + 6y = 30 → y = 5
→ y-int = (0, 5)

✔ Fill in:
x-int = -6
y-int = 5

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✔ 4) 4x + 3y = -9

x-intercept (set y = 0):
4x + 0 = -9 → x = -9/4 = -2.25
→ x-int = (-2.25, 0)

y-intercept (set x = 0):
0 + 3y = -9 → y = -3
→ y-int = (0, -3)

✔ Fill in:
x-int = -2.25 or -9/4
y-int = -3

*(Note: You can write as fraction or decimal — both are acceptable unless specified.)*

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✔ 5) -3x + y = 6

x-intercept (set y = 0):
-3x + 0 = 6 → -3x = 6 → x = -2
→ x-int = (-2, 0)

y-intercept (set x = 0):
0 + y = 6 → y = 6
→ y-int = (0, 6)

✔ Fill in:
x-int = -2
y-int = 6

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✔ 6) 5x - 3y = 15

x-intercept (set y = 0):
5x - 0 = 15 → x = 3
→ x-int = (3, 0)

y-intercept (set x = 0):
0 - 3y = 15 → -3y = 15 → y = -5
→ y-int = (0, -5)

✔ Fill in:
x-int = 3
y-int = -5

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## 📊 How to Graph Each Line:
Once you have the x- and y-intercepts:

1. Plot the x-intercept point on the x-axis.
2. Plot the y-intercept point on the y-axis.
3. Draw a straight line connecting the two points.

Example for #1: Plot (8,0) and (0,4), draw line through them.

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## ✍️ Final Answers to Fill In:

1) x-int = 8, y-int = 4
2) x-int = 3, y-int = -9
3) x-int = -6, y-int = 5
4) x-int = -2.25 (or -9/4), y-int = -3
5) x-int = -2, y-int = 6
6) x-int = 3, y-int = -5

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📌 Pro Tip: Always double-check your intercepts by plugging them back into the original equation!

Let me know if you want help graphing any of these lines! 😊