Solving Linear Equations And Real-World Applications

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Solving Linear Equations and Real - World Applications 1) Given the number of hours a plane has flown at different points in time, calculate the slope of the line, derive the equation of the line, and use it to predict the number of flight hours in 2019 Answer: A) Choose the first and third points, since they coincide with labeled values on the axes. The first point is at (0,240000) and the third point is at (2.0, 216000) B) The slope is found by calculating change in y divided by change in x: (216000 – 240000) / (2.0 – 0) = - 12000 C) For the slope intercept form we also need the y - intercept. By inspection, we see that this is just the y - value of our first point (since x=0). y = mx + b y = - 12000x + 240000 D) In 2009 the plane is three years old. This means that in 2019 the plane will be thirteen years old. Thus plug x=13 into the equation found in part C. y = ( - 12000)(13) + 240000 y = 84000 2) The width of a rectangle is 5 inches shorter than its length. If the perimeter of the rectangle is 80 inches, find the length and width of the rectangle. Answer: A) W = L – 5 Width is 5 inches shorter than length 80 = 2L + 2W Given that perimeter is 80 inches 80 = 2L + 2(L – 5) 80 = 4L – 10 B) 4L = 90
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