Practice worksheet for converting linear equations to slope-intercept form.

It looks like you've uploaded a worksheet titled "Between the Lines" with 14 linear equations, and the instruction is to rewrite each equation in slope-intercept form, which is:

> y = mx + b

Where:
- m is the slope
- b is the y-intercept

Let’s go through each equation one by one, solve it step-by-step, and rewrite it in slope-intercept form.

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1. 2y = x

We want to solve for y:
- Divide both sides by 2:
$$
y = \frac{1}{2}x
$$
✔ Answer: $ y = \frac{1}{2}x $

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2. x + 6 = 0

This equation has no y term. Solve for x:
- $ x = -6 $
This is a vertical line. But vertical lines cannot be written in slope-intercept form because they have undefined slope.
⚠️ Not possible in slope-intercept form.

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3. y - 4 = x

Solve for y:
- Add 4 to both sides:
$$
y = x + 4
$$
✔ Answer: $ y = x + 4 $

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4. y - 5 = 0

Add 5 to both sides:
- $ y = 5 $
This is a horizontal line.
✔ Answer: $ y = 5 $ (slope = 0)

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5. -2x + 3y = 18

Solve for y:
- Add 2x to both sides:
$ 3y = 2x + 18 $
- Divide by 3:
$ y = \frac{2}{3}x + 6 $
✔ Answer: $ y = \frac{2}{3}x + 6 $

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6. y + x + 4 = 0

Solve for y:
- Subtract x and 4:
$ y = -x - 4 $
✔ Answer: $ y = -x - 4 $

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7. √(x) - y = 0

Note: This includes a square root of x, so it's not linear.
- $ \sqrt{x} = y $
But this is not a linear equation — it's nonlinear due to the square root.
✘ Cannot be written in slope-intercept form (not a straight line).

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8. 5 + y = 0

Solve for y:
- $ y = -5 $
✔ Answer: $ y = -5 $

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9. y + x = 4

Solve for y:
- $ y = -x + 4 $
✔ Answer: $ y = -x + 4 $

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10. -4x + 6y = -36

Solve for y:
- Add 4x to both sides:
$ 6y = 4x - 36 $
- Divide by 6:
$ y = \frac{4}{6}x - 6 = \frac{2}{3}x - 6 $
✔ Answer: $ y = \frac{2}{3}x - 6 $

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11. y + 4 = x

Solve for y:
- $ y = x - 4 $
✔ Answer: $ y = x - 4 $

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12. 2x - 3y = 18

Solve for y:
- Subtract 2x:
$ -3y = -2x + 18 $
- Divide by -3:
$ y = \frac{2}{3}x - 6 $
✔ Answer: $ y = \frac{2}{3}x - 6 $

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13. x - 6 = 0

Solve for x:
- $ x = 6 $
This is a vertical line.
⚠️ Not possible in slope-intercept form.

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14. 20x + 30y = 180

Solve for y:
- Subtract 20x:
$ 30y = -20x + 180 $
- Divide by 30:
$ y = -\frac{20}{30}x + \frac{180}{30} = -\frac{2}{3}x + 6 $
✔ Answer: $ y = -\frac{2}{3}x + 6 $

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✔ Final Answers (in slope-intercept form):

| Problem | Slope-Intercept Form |
|--------|------------------------|
| 1 | $ y = \frac{1}{2}x $ |
| 2 | ✘ Not possible (vertical line) |
| 3 | $ y = x + 4 $ |
| 4 | $ y = 5 $ |
| 5 | $ y = \frac{2}{3}x + 6 $ |
| 6 | $ y = -x - 4 $ |
| 7 | ✘ Not possible (nonlinear) |
| 8 | $ y = -5 $ |
| 9 | $ y = -x + 4 $ |
| 10 | $ y = \frac{2}{3}x - 6 $ |
| 11 | $ y = x - 4 $ |
| 12 | $ y = \frac{2}{3}x - 6 $ |
| 13 | ✘ Not possible (vertical line) |
| 14 | $ y = -\frac{2}{3}x + 6 $ |

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🔍 Notes:

- Only linear equations with y as a function of x can be written in slope-intercept form.
- Vertical lines (x = constant) and non-linear equations (like those with $ \sqrt{x} $) cannot be expressed in this form.
- Always isolate y on one side, then simplify.

Let me know if you'd like a printed version or a table format!