The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8500 ​ft, the liquid boils at 199.95 degree

Question

The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8500 ​ft, the liquid boils at 199.95 degrees F. At an altitude of 4300 ​ft, the liquid boils at 205.41 degrees F. Write an equation giving the boiling point b of the​ liquid, in degrees​ Fahrenheit, in terms of altitude​ a, in feet. What is the boiling point of the liquid at 2600 ​ft?
Write an equation.
(Use integers or decimals for any numbers in the​ expression.)

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Katherine 2 weeks 2021-09-10T11:53:35+00:00 1 Answer 0

Answers ( )

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    2021-09-10T11:54:45+00:00

    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 y = mx + b.

    As the question specifies to use a for altitude and b for boiling point, change the variables equation to b = ma + c

    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 m = \frac{y_{2} - y_{1}  }{x_{2} - x_{1} } 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.

    m = \frac{b_{2} - b_{1}  }{a_{2} - a_{1} }

    m = \frac{205.41 - 199.95 }{4300 - 8500}

    m = \frac{5.46 }{-4200}

    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.

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