###### Example4.5.11

The conversion formula for a Celsius temperature into Fahrenheit is $$F=\frac{9}{5}C+32\text{.}$$ This appears to be in slope-intercept form, except that $$x$$ and $$y$$ are replaced with $$C$$ and $$F\text{.}$$ Suppose you are asked to graph this equation. How will you proceed? You could make a table of values as we do in Section 4.2 but that takes time and effort. Since the equation here is in slope-intercept form, there is a nicer way.

Since this equation is for starting with a Celsius temperature and obtaining a Fahrenheit temperature, it makes sense to let $$C$$ be the horizontal axis variable and $$F$$ be the vertical axis variable. Note the slope is $$\frac{9}{5}$$ and the $$y$$-intercept is $$(0,32)\text{.}$$

1. Set up the axes using an appropriate window and labels. Considering the freezing and boiling temperatures of water, it's reasonable to let $$C$$ run through at least $$0$$ to $$100\text{.}$$ Similarly it's reasonable to let $$F$$ run through at least $$32$$ to $$212\text{.}$$

2. Plot the $$y$$-intercept, which is at $$(0,32)\text{.}$$

3. Starting at the $$y$$-intercept, use slope triangles to reach the next point. Since our slope is $$\frac{9}{5}\text{,}$$ that suggests a “run” of $$5$$ and a rise of $$9$$ might work. But as Figure 4.5.12 indicates, such slope triangles are too tiny. Since $$\frac{9}{5}=\frac{90}{50}\text{,}$$ we can try a “run” of $$50$$ and a rise of $$90\text{.}$$