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The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8100 ​ft, the liquid boils at 203.66 degrees F. At an altitude of 4700 ​ft, the liquid boils at 208.42 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?

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sqdancefan

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Answer:

  • b = -0.0014a +215
  • 211.36 °F

Step-by-step explanation:

We are given two points: (a, b) = (8100, 203.66) and (4700, 208.42). We can use these in the 2-point form of the equation for a line

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1 . . . . . . line through (x1, y1) and (x2, y2)

Using the given values, we have ...

  b = (208.42 -203.66)/(4700 -8100)(a -8100) +203.66

  b = 4.76/-3400(a -8100) +203.66

  b = -0.0014a +215 . . . . . simplify

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At 2600 ft, the boiling point is ...

  b = -0.0014(2600) +215 = 211.36 °F

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