3. The table below lists temperatures measured in Fahrenheit and Celsius. [26 pts] | Celsius Degrees | 0 | 20 | 30 | 50 | 70 | 90 | 100 | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | Fahrenheit Degrees | 32 | 68 | 86 | 122 | 158 | 194 | 212 | a. Find a linear model to determine the temperature in degrees Fahrenheit as a function of temperature in degrees Celsius. [8 pts] b. According to your model, what is the temperature in degrees Fahrenheit for a temperature of 62 degrees Celsius? [5 pts] c. What is the practical significance of the slope and the y-intercept in your model? [5 pts] d. Sketch a labeled graph of your model. [8 pts]
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First, we need to find a linear model to determine the temperature in degrees Fahrenheit as a function of temperature in degrees Celsius. We can use the formula F = mC + b, where F is the temperature in Fahrenheit, C is the temperature in Celsius, m is the slope, Show more…
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The table shows equivalent temperatures in degrees Celsius and degrees Fahrenheit. $$\begin{array}{c|c|c|c|c|c}\circ \mathrm{F} & -40 & 32 & 59 & 95 & 212 \\\hline^{\circ} \mathrm{C} & -40 & 0 & 15 & 35 & 100\end{array}$$ (a) Plot the data by having the $x$ -axis correspond to Fahrenheit temperature and the $y$ -axis to Celsius temperature. What type of relation exists between the data? (b) Find a function $C$ that uses the Fahrenheit temperature $x$ to calculate the corresponding Celsius temperature. Interpret the slope. (c) What is a temperature of $83^{\circ} \mathrm{F}$ in degrees Celsius?
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The following graph shows the relationship between Fahrenheit temperature and Celsius temperature. a. Determine the slope of the line. b. Determine the equation of the line in slope-intercept form, where F is a function of C. c. Describe how F changes when C changes by 1 unit. d. Interpret F(0). e. Interpret F(C) = 0. f. Determine the equation of the relationship, where C is a function of F. g. Sketch the graph of y = C(F) to the left. h. Interpret C(0). i. Interpret C(F) = 0. j. Describe how C changes when F changes by 1 unit.
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The graph of Fahrenheit temperature, $^{\circ} \mathrm{F}$, as a function of Celsius temperature, $^{\circ} \mathrm{C}$, is a line. You know that $212^{\circ} \mathrm{F}$ and $100^{\circ} \mathrm{C}$ both represent the temperature at which water boils. Similarly, $32^{\circ} \mathrm{F}$ and $0^{\circ} \mathrm{C}$ both represent water's freezing point. (a) What is the slope of the graph? (b) What is the equation of the line? (c) Use the equation to find what Fahrenheit temperature corresponds to $20^{\circ} \mathrm{C}$ (d) What temperature is the same number of degrees in both Celsius and Fahrenheit?
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