Which equation represents function of a dial setting

Question

the interior temperature of a gas oven is determined by its dial setting, which goes from 1(lowest) to 10 (highest).The relationship between the dial setting N and the corresponding temperature T(N) is linear. When the dial setting is 2, the temperature is 150^C, and when the dial setting is 6, the temperature is 202^C. Which function represents the temperature as a function of the dial setting?

Answer 1

You have two points, (2, 150) and (6, 202).  You only need two points to define a line.

 

f(x) = mx + b

 

m = slope and b = y-intercept.  In this case, the equation is:

 

T(N) = mN + b

 

m = (y₂ - y₁)/(x₂ - x₁) = (202-150)/(6-2) = 52/4 = 13

 

So we have so far T(N) = 13N + b.  To find b, plug in either point and solve for b.  I'll use (2, 150):

 

T(N) = 13N + b

150 = 13*2 + b

150 = 26 + b

124 = b

 

Final equation:

 

T(N) = 13N + 124