The relationship between Celsius $$ \left({ }^{\circ} \mathrm{C} ight) $$ and Fahrenheit $$ \left({ }^{\circ} \mathrm{F} ight) $$ degrees of measuring temperature is linear. Find a linear equation relating $$ { }^{\circ} \mathrm{C} $$ and $$ { }^{\circ} \mathrm{F} $$ if $$ 0^{\circ} \mathrm{C} $$ corresponds to $$ 32{ }^{\circ} \mathrm{F} $$ and $$ 30^{\circ} \mathrm{C} $$ corresponds to $$ 86^{\circ} \mathrm{F} $$. Use the equation to find the Celsius measure of $$ 74^{\circ} \mathrm{F} $$. Choose the correct equation below. $$ \begin{array}{ll} ext { A. }{ }^{\circ} \mathrm{C}=\frac{5}{9}\left({ }^{\circ} \mathrm{F}+32 ight) & ext { B. }{ }^{\circ} \mathrm{C}=\frac{9}{5}\left({ }^{\circ} \mathrm{F}+32 ight) \ ext { C. }{ }^{\circ} \mathrm{C}=\frac{9}{5}\left({ }^{\circ} \mathrm{F}-32 ight) & ext { D. }{ }^{\circ} \mathrm{C}=\frac{5}{9}\left({ }^{\circ} \mathrm{F}-32 ight)\end{array} $$

Question

The relationship between Celsius $$ \left({ }^{\circ} \mathrm{C}ight) $$ and Fahrenheit $$ \left({ }^{\circ} \mathrm{F}ight) $$ degrees of measuring temperature is linear. Find a linear equation relating $$ { }^{\circ} \mathrm{C} $$ and $$ { }^{\circ} \mathrm{F} $$ if $$ 0^{\circ} \mathrm{C} $$ corresponds to $$ 32{ }^{\circ} \mathrm{F} $$ and $$ 30^{\circ} \mathrm{C} $$ corresponds to $$ 86^{\circ} \mathrm{F} $$. Use the equation to find the Celsius measure of $$ 74^{\circ} \mathrm{F} $$. Choose the correct equation below. $$ \begin{array}{ll}	ext { A. }{ }^{\circ} \mathrm{C}=\frac{5}{9}\left({ }^{\circ} \mathrm{F}+32ight) & 	ext { B. }{ }^{\circ} \mathrm{C}=\frac{9}{5}\left({ }^{\circ} \mathrm{F}+32ight) \ 	ext { C. }{ }^{\circ} \mathrm{C}=\frac{9}{5}\left({ }^{\circ} \mathrm{F}-32ight) & 	ext { D. }{ }^{\circ} \mathrm{C}=\frac{5}{9}\left({ }^{\circ} \mathrm{F}-32ight)\end{array} $$

UpStudy AI · Accepted Answer

To determine the correct linear equation relating Celsius ($$^{\circ}\mathrm{C}$$) and Fahrenheit ($$^{\circ}\mathrm{F}$$) temperatures, let's analyze the given data points and the standard conversion formulas.

### Given Data:
1. **Point 1:** $$0^{\circ}\mathrm{C} = 32^{\circ}\mathrm{F}$$
2. **Point 2:** $$30^{\circ}\mathrm{C} = 86^{\circ}\mathrm{F}$$

### Standard Conversion Formulas:
1. From Fahrenheit to Celsius:
   $$
   ^{\circ}\mathrm{C} = \frac{5}{9} \left( ^{\circ}\mathrm{F} - 32 \right)
   $$
2. From Celsius to Fahrenheit:
   $$
   ^{\circ}\mathrm{F} = \frac{9}{5} \left( ^{\circ}\mathrm{C} \right) + 32
   $$

### Evaluating the Options:
Let's test **Option D** since it aligns with the standard Fahrenheit to Celsius conversion.

**Option D:** 
$$
^{\circ}\mathrm{C} = \frac{5}{9} \left( ^{\circ}\mathrm{F} - 32 \right)
$$

**Verification with Given Data:**

1. **For $$0^{\circ}\mathrm{C}$$:**
   $$
   ^{\circ}\mathrm{C} = \frac{5}{9} (32 - 32) = \frac{5}{9} \times 0 = 0^{\circ}\mathrm{C}
   $$
   *Matches the given data.*

2. **For $$30^{\circ}\mathrm{C}$$:**
   $$
   30 = \frac{5}{9} (86 - 32) \implies 30 = \frac{5}{9} \times 54 \implies 30 = 30
   $$
   *Matches the given data.*

Since **Option D** correctly maps both data points, it is the correct equation.

### Using the Equation to Find Celsius for $$74^{\circ}\mathrm{F}$$:

$$
^{\circ}\mathrm{C} = \frac{5}{9} (74 - 32) = \frac{5}{9} \times 42 = \frac{210}{9} = 23.\overline{3}^{\circ}\mathrm{C}
$$

So, $$74^{\circ}\mathrm{F}$$ corresponds to approximately $$23.\overline{3}^{\circ}\mathrm{C}$$ or $$23 \frac{1}{3}^{\circ}\mathrm{C}$$.

### **Answer:**

**D.** $$^{\circ}\mathrm{C} = \frac{5}{9} \left( ^{\circ}\mathrm{F} - 32 \right)$$

Using this equation, $$74^{\circ}\mathrm{F}$$ corresponds to $$23 \frac{1}{3}^{\circ}\mathrm{C}$$.
The correct equation is $$ ^{\circ}\mathrm{C} = \frac{5}{9} \left( ^{\circ}\mathrm{F} - 32 \right) $$. Using this, $$74^{\circ}\mathrm{F}$$ is equal to $$23 \frac{1}{3}^{\circ}\mathrm{C}$$.

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