Question

excited about the success of celebrity stamps, post office officials were rumored to have put forth a plan to institute two new types of thermometers. on these new scales, °e represents degrees elvis and °m represents degrees madonna. if it is known that 30°e = 25°m, 310°e = 125°m, and degrees elvis is linearly related to degrees madonna, write an equation expressing e in terms of m.

e = □
(use integers or decimals for any numbers in the expression. do not include the degree symbol in your answer. do not factor.)

Explanation:

Step1: Define linear equation form

Let the linear relationship be $E = mM + b$, where $m$ is the slope and $b$ is the intercept.

Step2: Set up two equations from given points

Substitute $(M_1, E_1)=(25, 30)$ and $(M_2, E_2)=(125, 310)$:

1. $30 = 25m + b$
2. $310 = 125m + b$

Step3: Calculate slope $m$

Subtract equation 1 from equation 2:
$$310 - 30 = (125m + b) - (25m + b)$$
$$280 = 100m$$
$$m = \frac{280}{100} = 2.8$$

Step4: Calculate intercept $b$

Substitute $m=2.8$ into $30 = 25m + b$:
$$30 = 25\times2.8 + b$$
$$30 = 70 + b$$
$$b = 30 - 70 = -40$$

Step5: Write final equation

Substitute $m=2.8$ and $b=-40$ into $E = mM + b$.

Answer:

$E = 2.8M - 40$