# M:C:MC:15

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When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure *p* in pounds per square inch at a depth of *d* feet below the surface?

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Choice B is correct. To determine the linear model, one can first determine the rate at which the pressure due to the atmosphere and surrounding water is increasing as the depth of the diver increases. Calculating this gives or 0.44. Then one needs to determine the pressure due to the atmosphere or, in other words, the pressure when the diver is at a depth of 0. Solving the equation gives Therefore, the model that can be used to relate the pressure and the depth is

Choice A is not the correct answer. The rate is calculated correctly, but the student may have incorrectly used the ordered pair rather than to calculate the pressure at a depth of 0 feet.

Choice C is not the correct answer. The rate here is incorrectly calculated by subtracting 20.9 and 18.7 and *not* dividing by 5. The student then uses the coordinate pair and in conjunction with the incorrect slope of 2.2 to write the equation of the linear model.

Choice D is not the correct answer. The rate here is incorrectly calculated by subtracting 20.9 and 18.7 and *not* dividing by 5. The student then uses the coordinate pair and in conjunction with the incorrect slope of 2.2 to write the equation of the linear model.

Students must construct a linear equation to represent a real-world situation.