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 40°E = 25°M, and 280°E = 125°M; and degrees Elvis is linearly related to degrees Madonna, write an equation expressing E in terms of M.

"E in terms of M" is like "y in terms of x", so let M be the independent variable and let E be the dependent variable.

Thus we have two points on this linear graph:
(25, 40) and (125, 280)
Use m=(E2 - E1)/(M2 - M1) to get the slope.
Sub slope and one of the points into
E = mM + b to find b.

To solve this problem, we need to express Elvis degrees (E) in terms of Madonna degrees (M) using the given information.

First, let's establish the relationship between the two scales. From the information provided, we know that 40°E is equivalent to 25°M and 280°E is equivalent to 125°M.

To find the linear relationship between E and M, we can use the slope-intercept form of a linear equation, which is given by:

y = mx + b

In this case, E represents y, M represents x, and b represents the y-intercept (the value of E when M is zero). We need to find the value of the slope (m) and the y-intercept (b).

Let's start by finding the slope (m). The slope of a line can be determined using the formula:

m = (change in y) / (change in x)

To find the change in y, we subtract the Elvis degree values: 280°E - 40°E = 240°E.
To find the change in x, we subtract the Madonna degree values: 125°M - 25°M = 100°M.

So, the slope (m) is 240°E / 100°M, which can be simplified to 12/5 or 2.4.

Now, let's determine the y-intercept (b). We can use one of the given data points: 40°E = 25°M.

When M is 25°M, we need to find the corresponding E value. We can use the equation y = mx + b, substituting M = 25°M, E = 40°E, and m = 2.4:

40°E = 2.4 * 25°M + b

Solving for b, we have:

40°E - 60°E = b
b = -20°E

So, the y-intercept (b) is -20°E.

Now, we can write the equation expressing E in terms of M:

E = 2.4M - 20

Therefore, the equation expressing E in terms of M is E = 2.4M - 20.