Question

The temperature at dawn one morning was –6 °C. It increased at a constant rate of 2 °C per hour after that. Which equation describes t, the time in hours since dawn, in terms of C, the temperature in degrees Celsius?

Answer 1

`t= \frac12C +3`

Explanation:

Let's first write the data you have in an equation form:

`C= -6 + 2t`. When t = 0, at dawn, you get -6°C so we're good. But you've ben asked the inverse relationship, so let's solve for t instead.

`-6+2t = C\\2t = C+6\\t= \frac12(C+6)\\t= \frac12C +3`

Last two are both viable solution, only difference is in form. I do prefer the last option since it makes it easiest at a glance to answer to the question "at what time there's a temperature of 0°C?"