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Question 1049142: I'm having trouble breaking down this word problem.
Problem- A new temperature scale has been introduced called Sandstrum and denoted by S. Here are two comparisons to the Celsius scale. Water freezes at 0 degrees Celsius= -125 degrees S and water boils at 100 degrees Celsius=-50 degrees S.
A.)Find an equation for the line that captures the relationship. Let C be the independent (x) variable. Leave non-whole numbers fractions.
B.) What is the temperature (to the nearest degree in Sandstrum (S) when it is 72 degrees Celsius.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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