Example 1

Example 1. In Canada and Mexico, weather reports report temperature using the Centigrade (or Celsius) scale.   In the US, temperature is reported using the Fahrenheit scale.   To convert temperature C to temperature F, we use the formula [latex]F=\frac{9}{5}C+32[/latex].   When the temperature C is 23°, what is the temperature F?

Answer:

[latex]\begin{align}&F=\frac{9}{5}C+32\\&F=\frac{9}{5}(23)+32\\&F=41.4+32\\&F=73.4\\\end{align}[/latex]

Thus the temperature F is 73.4°. Notice that we used the correct order of operations here, performing the multiplication before the addition. Here we call the 23° the input value and the 73.4° the output value.  (In algebra class, we call the set of input values the “domain” and the set of output values the “range”.) When we graph a formula, we will put the input value on the horizontal axis, sometimes called the x-axis, and the output value on the vertical axis, sometimes called the y-axis. We can use different letters for the variables besides x and y, but when we think of the formula graphically, we must be clear about which variable plays the role of x and which plays the role of y. (You should be able to do these graphs by hand as well as with a spreadsheet.)

Formula input and output
C	F
23	73.4
0	32
10	50
20	68
30	86
40	104