I'll do problem 1 to get you started.
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1a. Pick any four ordered pairs of the form (x,y) such that y = 2x. In other words, these points are all on the line y = 2x.
Four such points are: (1,2), (2,4), (3,6) and (4,8)
There are infinitely many points to pick from.
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1b. Similar to the first problem, but now y = x+5. Whatever the x coordinate is, we add 5 to it to get the y coordinate.
Four such points are: (0,5), (1,6), (2,7), (3,8)
There are infinitely many points
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1c. Similar idea as before, but now y = x-4
Four points on this line are: (0,-4), (1,-3), (2,-2), (3,-1)
There are infinitely many points.
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1d. Take half of the x coordinate to get the y coordinate. The equation is y = x/2 or y = (1/2)x or y = 0.5x
Four points on this line are: (2,1), (4,2), (6,3), (8,4)
There are infinitely many points.
