How can I find a scale where 30(x) = 250 and 250(x) = 500

Question

I'm trying to find apply a scale for a knob where an angle of 30 degrees equals 250 and 250 degrees = 500, could you guys help me solve this?

If this problem is too basic for this group, please point me where I can ask these questions. Thanks in advance.

Answer 1

I assume you're looking for a linear scale. Let $T$ be the temperature and $x$ the angle; you'll need a formula of the form

$$T = ax + b$$

(where $b$ is the 'initial temperature' corresponding to an angle of 0 degrees)

Plugging in both conditions:

$$500 = 250a + b$$

$$250 = 30a + b$$

and subtracting gives:

$$250 = 220a$$

Can you take it from there?