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bonufazy [111]
2 years ago
15

Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a

70-hour review course average a score of 749. Find a linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course. Round your answer to the tenths place.
Mathematics
1 answer:
Alina [70]2 years ago
4 0

Given:

30-hour review course average a score of 620 on that exam.

70-hour review course average a score of 749.

To find:

The linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course.

Solution:

Let x be the number of hours of review course and y be the average score on that exam.

30-hour review course average a score of 620 on that exam. So, the linear function passes through the point (30,620).

70-hour review course average a score of 749. So, the linear function passes through the point (70,749).

The linear function passes through the points (30,620) and (70,749). So, the linear equation is:

y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)

y-620=\dfrac{749-620}{70-30}(x-30)

y-620=\dfrac{129}{40}(x-30)

y-620=\dfrac{129}{40}(x)-\dfrac{129}{40}(30)

y-620=\dfrac{129}{40}(x)-\dfrac{387}{4}

Adding 620 on both sides, we get

y=\dfrac{129}{40}x-\dfrac{387}{4}+620

y=\dfrac{129}{40}x+\dfrac{2480-387}{4}

y=\dfrac{129}{40}x+\dfrac{2093}{4}

We need to find the y-value for x=57.

y=\dfrac{129}{40}(57)+\dfrac{2093}{4}

y=183.825+523.25

y=707.075

y\approx 707.1

Therefore, the required linear equation for the given situation is y=\dfrac{129}{40}x+\dfrac{2093}{4} and the average score for persons taking a 57-hour review course is 707.1.

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