Rearranging Formulae: Complete with ease | airSlate SignNow - Free Printable

Let's solve each of the equations for the specified variable. I'll go through them one by one, showing the steps clearly.

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1. $ y = mx + b $ → Solve for $ b $

We want to isolate $ b $.
Subtract $ mx $ from both sides:

$$
b = y - mx
$$

✔ Answer: $ b = y - mx $

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2. $ y = mx + b $ → Solve for $ m $

We want to isolate $ m $.
Subtract $ b $ from both sides:

$$
y - b = mx
$$

Now divide both sides by $ x $ (assuming $ x \ne 0 $):

$$
m = \frac{y - b}{x}
$$

✔ Answer: $ m = \frac{y - b}{x} $

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3. $ V = lwh $ → Solve for $ w $

We want to isolate $ w $.
Divide both sides by $ lh $:

$$
w = \frac{V}{lh}
$$

✔ Answer: $ w = \frac{V}{lh} $

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4. $ V = \pi r^2 h $ → Solve for $ h $

Divide both sides by $ \pi r^2 $:

$$
h = \frac{V}{\pi r^2}
$$

✔ Answer: $ h = \frac{V}{\pi r^2} $

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5. $ v_f = v_i + at $ → Solve for $ v_0 $

Note: $ v_0 $ is likely a typo and should be $ v_i $. Assuming that:

$$
v_i = v_f - at
$$

✔ Answer: $ v_i = v_f - at $

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6. $ v_f = v_i + at $ → Solve for $ a $

Subtract $ v_i $ from both sides:

$$
v_f - v_i = at
$$

Divide by $ t $:

$$
a = \frac{v_f - v_i}{t}
$$

✔ Answer: $ a = \frac{v_f - v_i}{t} $

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7. $ P = F/A $ → Solve for $ I $

Wait — this equation is $ P = F/A $, but you're asked to solve for $ I $? That doesn't make sense unless $ I $ is related.

But in physics, pressure $ P = F/A $, so there’s no $ I $ here.

Possibility: This might be a typo. If $ P = F/A $, then solving for $ F $:

$$
F = PA
$$

Or if it's meant to be $ I = P $ or something else?

But based on what's written: $ P = F/A $, and we’re to solve for $ I $? That can’t be done unless $ I $ is defined.

Assuming this is a typo and it's meant to be solve for $ F $:

$$
F = PA
$$

✔ Answer (assuming typo): $ F = PA $

If not, please clarify.

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8. $ x = x_0 + v_0 t + \frac{1}{2} a t^2 $ → Solve for $ x_0 $

Subtract $ v_0 t + \frac{1}{2} a t^2 $ from both sides:

$$
x_0 = x - v_0 t - \frac{1}{2} a t^2
$$

✔ Answer: $ x_0 = x - v_0 t - \frac{1}{2} a t^2 $

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9. $ v = f\lambda $ → Solve for $ v $

This is already solved for $ v $. But let's check.

The equation is $ v = f\lambda $, and we're to solve for $ v $? That’s already done.

So unless it's asking to express $ v $ in terms of $ f $ and $ \lambda $, which it is, then:

✔ Answer: $ v = f\lambda $

(No change needed.)

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10. $ W = Fd $ → Solve for $ d $

Divide both sides by $ F $:

$$
d = \frac{W}{F}
$$

✔ Answer: $ d = \frac{W}{F} $

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11. $ F = ma $ → Solve for $ m $

Divide both sides by $ a $:

$$
m = \frac{F}{a}
$$

✔ Answer: $ m = \frac{F}{a} $

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12. $ F = mg $ → Solve for $ g $

Divide both sides by $ m $:

$$
g = \frac{F}{m}
$$

✔ Answer: $ g = \frac{F}{m} $

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13. $ E = mc^2 $ → Solve for $ c $

Divide both sides by $ m $:

$$
c^2 = \frac{E}{m}
$$

Take square root of both sides:

$$
c = \sqrt{\frac{E}{m}}
$$

✔ Answer: $ c = \sqrt{\frac{E}{m}} $

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14. $ p = mv $ → Solve for $ m $

Divide both sides by $ v $:

$$
m = \frac{p}{v}
$$

✔ Answer: $ m = \frac{p}{v} $

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15. $ V = IR $ → Solve for $ R_0 $

Wait — the equation is $ V = IR $, and we're to solve for $ R_0 $? But $ R_0 $ isn't in the equation.

Possibility: Typo. Likely meant to solve for $ R $.

So:

$$
R = \frac{V}{I}
$$

✔ Answer (assuming typo): $ R = \frac{V}{I} $

If $ R_0 $ is intended to be $ R $, then same thing.

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## ✔ Final Answers Summary:

| Problem | Equation | Solve for | Answer |
|--------|---------|-----------|--------|
| 1 | $ y = mx + b $ | $ b $ | $ b = y - mx $ |
| 2 | $ y = mx + b $ | $ m $ | $ m = \frac{y - b}{x} $ |
| 3 | $ V = lwh $ | $ w $ | $ w = \frac{V}{lh} $ |
| 4 | $ V = \pi r^2 h $ | $ h $ | $ h = \frac{V}{\pi r^2} $ |
| 5 | $ v_f = v_i + at $ | $ v_i $ | $ v_i = v_f - at $ |
| 6 | $ v_f = v_i + at $ | $ a $ | $ a = \frac{v_f - v_i}{t} $ |
| 7 | $ P = F/A $ | $ I $ | ✘ Invalid variable; likely typo — $ F = PA $ |
| 8 | $ x = x_0 + v_0 t + \frac{1}{2} a t^2 $ | $ x_0 $ | $ x_0 = x - v_0 t - \frac{1}{2} a t^2 $ |
| 9 | $ v = f\lambda $ | $ v $ | $ v = f\lambda $ |
| 10 | $ W = Fd $ | $ d $ | $ d = \frac{W}{F} $ |
| 11 | $ F = ma $ | $ m $ | $ m = \frac{F}{a} $ |
| 12 | $ F = mg $ | $ g $ | $ g = \frac{F}{m} $ |
| 13 | $ E = mc^2 $ | $ c $ | $ c = \sqrt{\frac{E}{m}} $ |
| 14 | $ p = mv $ | $ m $ | $ m = \frac{p}{v} $ |
| 15 | $ V = IR $ | $ R_0 $ | ✘ Likely typo — $ R = \frac{V}{I} $ |

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⚠️ Note: Problems 7 and 15 contain variables ($ I $ and $ R_0 $) not present in the original equations. These are likely typos. The correct interpretations are:
- #7: Solve for $ F $ → $ F = PA $
- #15: Solve for $ R $ → $ R = \frac{V}{I} $

Let me know if you'd like these corrected in a printable format!