Problem
Measuring Temperature. The two most commonly used scales for measuring temperature are the Fahrenheit and Celsius scales. If you let $y$ denote the Fahrenheit temperature and $x$ denote Celsius temperature, you can express the relationship between those two scales with the linear equation $y=32+1.8 x$. a. Determine the $y$-intercept $b_{0}$ and the slope $b_{1}$. \[ \begin{array}{l} b_{0}=32 \\ b_{1}=1.8 \end{array} \] b. Find the Fahrenheit temperature corresponding to the Celsius temperature $-37^{\circ}$. degrees c. Find the Fahrenheit temperature corresponding to the Celsius temperature $0^{\circ}$. degrees d. Find the Fahrenheit temperature corresponding to the Celsius temperature $24^{\circ}$. degrees e. Find the Fahrenheit temperature corresponding to the Celsius temperature $100^{\circ}$. degrees f. Graph the linear equation $y=32+1.8 x$, using the four points found in (b), (c), (d) and (e). g. Apply the graph obtained in part (f) to estimate visually the Fahrenheit temperature corresponding to a Celsius temperature of $38^{\circ}$. Then calculate that temperature exactly by using the linear equation $y=32+1.8 x$. The exact Fahrenheit temperature corresponding to the Celsius temperature of $38^{\circ}$ is degrees
Solution
Step 1 ：Given the Celsius temperature as -37 degrees, we need to convert this to Fahrenheit. The formula to convert Celsius to Fahrenheit is \(y=32+1.8x\).
Step 2 ：Substitute -37 for x in the formula: \(y=32+1.8(-37)\).
Step 3 ：Simplify the expression to find the Fahrenheit temperature.
Step 4 ：Final Answer: \(-37^\circ C=\boxed{-34.6}^\circ F\)
