Hi,

I'm hoping someone can explain this problem to me..

In the xy-plane, does the point (4,12) line on the line k?

1) The point (1,7) lies on line k
2) The point (-2,2) lies on line k

If you haven't done so already, draw a number line. Use graph paper so you can make it accurate (you'll also have graph paper as your scratch paper on the test).

(1) Plot the point (1,7). Can you draw a line that also goes through (4,12)? Yes. Can you draw a line that does not go through (4,12)? Yes. So you can't tell from this statement alone. Eliminate A and D.

(2) Plot the point (-2,2) and IGNORE the point (1,7). Can you draw a line that also goes through (4,12)? Yes. Can you draw a line that does not go through (4,12)? Yes. So you can't tell from this statement alone. Eliminate B.

(1) AND (2) Draw a line between the points (1,7) and (-2,2). You now have a line with a specific slope and either that third point does or does not fall on that line - there's only one answer. Whether it does or does not, this info is still sufficient to answer the question (remember that for a yes/no question, no and yes are sufficient answers - only maybe is not a sufficient answer, as we had when we looked at the statements individually). If you want to test it, you can extend the line and see whether it hits (4,12) or you can calculate the slope and see if it works - but you really don't need to do this. The two points together give you only one possibility for the line, and therefore only one possible answer to the question. Sufficient.