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.

Answer 1

"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.