Question 1049142
basically, you are creating a straight line equation where the independent variable is c and the dependent variable is s.


s represents the temperature in sandstrum.
c represents the temperature in celsius.


you have 2 points of reference.


they are the freezing point of water and the boiling point of water.


when water freezes, the temperature is 0 degrees in celsius and -125 degrees in sandstrum.


when water boils, the temperature is 100 degrees in celsius and -50 degrees in sandstrum.


you have two coordinate points of reference.


(c1,s1) = (0,-125)
(c2,s2) = (100,-50)


the slope intercept form of a straight line equation is y = mx + b.
m is the slope.
b is the y-intercept.


the slope is equal to (y2-y1) / (x2-x1).
the y-intercept is the value of y when x is equal to 0.


if you replace y with s and x with c, your straight line equation becomes:


s = mc + b
m is the slope.
b is the s-intercept


the slope is equal to (s2-s1) / (c2-c1).
the s-intercept is the value of s when c is equal to 0.


it's the same equation as y = mx + b with only the names of the variables changed, where s is used in place of y and c is used in place of x.


your two points of reference are:


(c1,s1) = (0,-125)
(c2,s2) = (100,-50)


your s-intercept is the value of s when c is equal to 0.
that makes your s-intercept equal to -125.
that makes b = -125.


your slope is equal to (s2-s1) / (c2-c1) = (-50 - (-125)) / (100 - 0).
simplify that and your slope is equal to 75/100.
this can be simplified to 3/4.


your straight line equation of s = mx + b becomes s = 3/4 * c - 125.


when c is equal to 0, s is equal to -125.
this agrees with the freezing point of water expressed in sandstrum.


when c is equal to 100, s is equal to -50.
this agrees with the boiling point of water expressed in sandstrum.


part A solution is therefore s = 3/4 * c - 125.


when c = 72, s = 3/4 * 72 - 125 which becomes s = -71.


that's your part B solution.