Slope-Intercept Form Worksheet for practicing converting linear equations to slope-intercept form and writing equations from given slope and y-intercept.

Let's solve each problem step by step and explain the process.

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Part 1: Write each equation in slope-intercept form

Slope-intercept form is:
$$
y = mx + b
$$
where $ m $ is the slope and $ b $ is the y-intercept.

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#### ① $ 2x + 4y = 8 $

We want to solve for $ y $:

$$
4y = -2x + 8
$$
$$
y = \frac{-2x + 8}{4} = -\frac{1}{2}x + 2
$$

✔ Answer: $ y = -\frac{1}{2}x + 2 $

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#### ② $ 4 - 8x = 2y $

Solve for $ y $:

$$
2y = -8x + 4
$$
$$
y = \frac{-8x + 4}{2} = -4x + 2
$$

✔ Answer: $ y = -4x + 2 $

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#### ③ $ -12x + y = 8 $

Solve for $ y $:

$$
y = 12x + 8
$$

✔ Answer: $ y = 12x + 8 $

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#### ④ $ 2y - 6 = -6x $

Add 6 to both sides:

$$
2y = -6x + 6
$$
Divide by 2:

$$
y = -3x + 3
$$

✔ Answer: $ y = -3x + 3 $

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#### ⑤ $ 7 = 2x - y $

Solve for $ y $:

$$
-y = -2x + 7
$$
Multiply both sides by -1:

$$
y = 2x - 7
$$

✔ Answer: $ y = 2x - 7 $

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#### ⑥ $ 4y = 4x $

Divide both sides by 4:

$$
y = x
$$

✔ Answer: $ y = x $

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Part 2: Write the slope-intercept form given slope and y-intercept

Use: $ y = mx + b $

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#### ⑦ Slope = 3, y-intercept = -2

$$
y = 3x - 2
$$

✔ Answer: $ y = 3x - 2 $

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#### ⑧ Slope = -3, y-intercept = 7

$$
y = -3x + 7
$$

✔ Answer: $ y = -3x + 7 $

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#### ⑨ Slope = 0, y-intercept = -1

A zero slope means a horizontal line:

$$
y = 0x - 1 = -1
$$

✔ Answer: $ y = -1 $

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#### ⑩ Slope = $-\frac{1}{2}$, y-intercept = -2

$$
y = -\frac{1}{2}x - 2
$$

✔ Answer: $ y = -\frac{1}{2}x - 2 $

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#### ⑪ Slope = $-\frac{4}{5}$, y-intercept = 0

$$
y = -\frac{4}{5}x + 0 = -\frac{4}{5}x
$$

✔ Answer: $ y = -\frac{4}{5}x $

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#### ⑫ Slope = -1, y-intercept = -4

$$
y = -x - 4
$$

✔ Answer: $ y = -x - 4 $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| ① | $ y = -\frac{1}{2}x + 2 $ |
| ② | $ y = -4x + 2 $ |
| ③ | $ y = 12x + 8 $ |
| ④ | $ y = -3x + 3 $ |
| ⑤ | $ y = 2x - 7 $ |
| ⑥ | $ y = x $ |
| ⑦ | $ y = 3x - 2 $ |
| ⑧ | $ y = -3x + 7 $ |
| ⑨ | $ y = -1 $ |
| ⑩ | $ y = -\frac{1}{2}x - 2 $ |
| ⑪ | $ y = -\frac{4}{5}x $ |
| ⑫ | $ y = -x - 4 $ |

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🔍 Explanation of Key Concepts:

- Slope-intercept form: Always write as $ y = mx + b $
- To convert equations: isolate $ y $ on one side.
- When given slope and y-intercept, plug into $ y = mx + b $
- A slope of 0 gives a horizontal line (constant $ y $)
- A y-intercept of 0 means the line passes through the origin

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