To approach this problem, we will use the conversion formula between Celsius ($C$) and Fahrenheit ($F$):

$F = \frac{9}{5}C + 32$

Step 1: Find the Celsius equivalent when $F = 60$.

Using the formula, we solve for $C$ when $F = 60$:

$60 = \frac{9}{5}C + 32$

Subtract 32 from both sides:

$60 - 32 = \frac{9}{5}C$

$28 = \frac{9}{5}C$

Now, multiply both sides by $\frac{5}{9}$ to solve for $C$:

$C = 28 \times \frac{5}{9} = \frac{140}{9} \approx 15.56^\circ \text{C}$

So, when it is 60°F, the Celsius temperature is approximately $15.56^\circ C$. You can plot this point as (60, 15.56) on the graph.

Step 2: Find the Fahrenheit equivalent when $C = 60$.

Now, use the formula again to find $F$ when $C = 60$:

$F = \frac{9}{5} \times 60 + 32 = 108 + 32 = 140^\circ F$

So, when it is 60°C, the Fahrenheit temperature is $140^\circ F$. You can plot this point as (140, 60) on the graph.

Step 3: Would 100 degrees Fahrenheit give 40 degrees Celsius?

Let's check by solving for $C$ when $F = 100$:

$100 = \frac{9}{5}C + 32$

Subtract 32 from both sides:

$100 - 32 = \frac{9}{5}C$

$68 = \frac{9}{5}C$

Multiply by $\frac{5}{9}$ to solve for $C$:

$C = 68 \times \frac{5}{9} = \frac{340}{9} \approx 37.78^\circ C$

So, 100°F corresponds to approximately $37.78^\circ C$, not exactly 40°C. This is because the conversion between Fahrenheit and Celsius follows a precise formula, and the values do not align exactly at 100°F and 40°C.

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Would you like more details or have any other questions? Here are five related questions:

1. What is the general formula to convert from Celsius to Fahrenheit?
2. What temperature in Celsius corresponds to 32°F?
3. How can you calculate the inverse function for converting Fahrenheit to Celsius?
4. What is the physical meaning of the freezing and boiling points of water in both scales?
5. How does the Fahrenheit scale compare to the Kelvin scale in terms of increments?

Tip: Always subtract 32 before applying the fraction when converting Fahrenheit to Celsius.