Slope Intercept Form Worksheets with Answer Key - Free Printable

Let's solve each problem by converting the given slope-intercept form equations into standard form.

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🔷 Standard Form of a Linear Equation:

The standard form is:

$$
Ax + By + C = 0 \quad \text{or} \quad Ax + By = C
$$

Where:
- $ A, B, C $ are integers,
- $ A \geq 0 $ (if possible),
- $ A $ and $ B $ are not both zero,
- The greatest common divisor of $ A, B, C $ is 1 (if possible).

We'll convert each equation step-by-step.

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✔ Problem 1: $ y = \frac{5}{2}x - 5 $

Step 1: Eliminate fractions by multiplying every term by the denominator (2):

$$
2y = 5x - 10
$$

Step 2: Move all terms to one side:

$$
-5x + 2y + 10 = 0
$$

Step 3: Multiply by -1 to make $ A > 0 $:

$$
5x - 2y - 10 = 0 \quad \text{or} \quad 5x - 2y = 10
$$

✔ Answer: $ \boxed{5x - 2y = 10} $

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✔ Problem 2: $ y = \frac{3}{2}x + 3 $

Multiply by 2:

$$
2y = 3x + 6
$$

Move all terms:

$$
-3x + 2y - 6 = 0
$$

Multiply by -1:

$$
3x - 2y + 6 = 0 \quad \Rightarrow \quad 3x - 2y = -6
$$

✔ Answer: $ \boxed{3x - 2y = -6} $

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✔ Problem 3: $ 2y = 8x - 12 $

Move all terms to one side:

$$
-8x + 2y + 12 = 0
$$

Divide entire equation by 2 to simplify:

$$
-4x + y + 6 = 0
$$

Multiply by -1:

$$
4x - y - 6 = 0 \quad \Rightarrow \quad 4x - y = 6
$$

✔ Answer: $ \boxed{4x - y = 6} $

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✔ Problem 4: $ 5y = -\frac{3}{5}x + 3 $

Multiply every term by 5 to eliminate fraction:

$$
25y = -3x + 15
$$

Move all terms:

$$
3x + 25y - 15 = 0 \quad \Rightarrow \quad 3x + 25y = 15
$$

✔ Answer: $ \boxed{3x + 25y = 15} $

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✔ Problem 5: $ y = \frac{5}{4}x + 5 $

Multiply by 4:

$$
4y = 5x + 20
$$

Move terms:

$$
-5x + 4y - 20 = 0
$$

Multiply by -1:

$$
5x - 4y + 20 = 0 \quad \Rightarrow \quad 5x - 4y = -20
$$

✔ Answer: $ \boxed{5x - 4y = -20} $

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✔ Problem 6: $ y = 2x - 2 $

Move terms:

$$
-2x + y + 2 = 0
$$

Multiply by -1:

$$
2x - y - 2 = 0 \quad \Rightarrow \quad 2x - y = 2
$$

✔ Answer: $ \boxed{2x - y = 2} $

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✔ Problem 7: $ -2x + y = 4 $

This is already in standard form. But we want $ A \geq 0 $. So multiply by -1:

$$
2x - y = -4
$$

✔ Answer: $ \boxed{2x - y = -4} $

---

✔ Problem 8: $ y = 2x + 5 $

Move terms:

$$
-2x + y - 5 = 0
$$

Multiply by -1:

$$
2x - y + 5 = 0 \quad \Rightarrow \quad 2x - y = -5
$$

✔ Answer: $ \boxed{2x - y = -5} $

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✔ Problem 9: $ y = -2x + 7 $

Move terms:

$$
2x + y - 7 = 0 \quad \Rightarrow \quad 2x + y = 7
$$

✔ Answer: $ \boxed{2x + y = 7} $

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✔ Problem 10: $ y = \frac{1}{2}x + \frac{1}{2} $

Multiply by 2:

$$
2y = x + 1
$$

Move terms:

$$
-x + 2y - 1 = 0
$$

Multiply by -1:

$$
x - 2y + 1 = 0 \quad \Rightarrow \quad x - 2y = -1
$$

✔ Answer: $ \boxed{x - 2y = -1} $

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📌 Final Answers:

| # | Standard Form |
|---|----------------|
| 1 | $ 5x - 2y = 10 $ |
| 2 | $ 3x - 2y = -6 $ |
| 3 | $ 4x - y = 6 $ |
| 4 | $ 3x + 25y = 15 $ |
| 5 | $ 5x - 4y = -20 $ |
| 6 | $ 2x - y = 2 $ |
| 7 | $ 2x - y = -4 $ |
| 8 | $ 2x - y = -5 $ |
| 9 | $ 2x + y = 7 $ |
|10 | $ x - 2y = -1 $ |

Let me know if you'd like these written on the worksheet format!