Consider the three points (4,3) , (20,15) , and (48,36).
Part A
The model for direct variation is y = kx k = y/x {divided each side by x} If a point is on the same line, it should have the same y/x ratio, equaling the constant of variation, k. For the first point (4,3), the constant of variation is: k = (3) / (4) = 3/4 {reduced the constant of variation} The points that have a y/x ratio of 3/4 are: A.) (8,6) and D.) (4,3)
Part B
In part A, the constant of variation, k = y/x , was found to be 3/4 . Every point on the line has a ratio of the ycoordinates to the xcoordinates being 3/4, except the yintercept. At the yintercept, the value of x is 0. Therefore, if x is zero, then k=y/x would be undefined.
Part C
No. The equation y = 3x – 2 is not in the form of direct variation, which is y = kx, because of the constant term, 2.
Therefore, the ratio of the ycoordinate to the xcoordinate is not constant.
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