Answer:
b = -0.0013a + 211
Step-by-step explanation:
Since the relationship is linear, we can use a linear equation. The formula in slope-intercept form is [tex]y = mx + b[/tex].
As the question specifies to use a for altitude and b for boiling point, change the variables equation to [tex]b = ma + c[/tex]
b is the boiling point.
m is the slope.
a is the altitude.
c is the y-intercept.
To find the slope, we can use the equation [tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] except x is a and y is b.
The sets of information given are:
8500 ft, the liquid boils at 199.95° (This can be info set 1)
4300 ft, the liquid boils at 205.41° (This can be info set 2)
Substitute the info sets into the equation. The subscripts mean which info set to get the numbers from.
[tex]m = \frac{b_{2} - b_{1} }{a_{2} - a_{1} }[/tex]
[tex]m = \frac{205.41 - 199.95 }{4300 - 8500}[/tex]
[tex]m = \frac{5.46 }{-4200}[/tex]
m = -0.0013
Find the y-intercept by substituting m = -0.0013 and a random info set. I will use info set 1. Isolate c, the only variable.
b = ma + c
199.95 = (-0.0013)(8500) + c <= Simplify
199.95 = -11.05 + c
199.95 + 11.05 = -11.05 + 11.05 + c <=add 11.05 on both sides to isolate c
c = 211 <= y-intercept
Put the y-intercept and slope into the equation of a line:
b = ma + c
b = -0.0013a + 211 <= This is the equation for the problem.
