Data Analysis problem

*CALCULATOR REQUIRED

The following table shows points (x, y) on the same line. Which of the following choices shows variable y in terms of variable x for the line?

A. y = -5x/2 - 12.15
B. y = -2x/5 - 2.28
C. y = -2x/5 - 1.48
D. y = -5x/2 - 11.35


Since every point on the table (x, y) shares the same line, we can determine the slope of the line using any pair of three available points. We will use the first two for convenience. The slope is found by the formula (change in y) / (change in x) = [0 - 0.4] / (-3.7 - (-4.7)] = -0.4 / 1 = -2/5. This rules out choices A and D. We now have the equation in the form y = -2x/5 + b, where b is the y-intercept or point on the line where x = 0, that is, (0, b). Using the point-slope formula (and the first point on the table) we have the equation as y - 0.4 = -2/5[x - (-4.7)], which simplifies to y = -2x/5 - 1.88 + 0.4, or y = -2x/5 - 1.48. Be sure to check this equation with all of the given points x above to see if you are getting the corresponding y values. Thus the correct answer choice is (C).

You may also plug in each equation in the answer choices if you forget how to set up your equation, but it may take extra time. You may, however, take a shortcut after you find the correct slope -2/5 to check answers (B) and (C) with the table values to find the correct y-intercept.

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