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Recall from geometry that if two lines are perpendicular to the same line, these two lines
\n" ); document.write( "are parallel. You know that the y-axis is perpendicular to the x-axis. And the problem
\n" ); document.write( "tells you that of the two graphs you are to make one is parallel to the y-axis and the
\n" ); document.write( "other is perpendicular to the x-axis. Therefore, your graphs will both be parallel to
\n" ); document.write( "the y-axis and both will be perpendicular to the x-axis. That means that your graphs will
\n" ); document.write( "be vertical lines, just as the y-axis is. Now ask yourself, \"How many values of y will these
\n" ); document.write( "two vertical graphs have?\" The answer is that each will have lots of them ... an infinite number
\n" ); document.write( "because each vertical lines has a different y-value for each of the heights it goes through.
\n" ); document.write( "But if you ask yourself, \"How many values of x will each graph have?\" you get an entirely
\n" ); document.write( "different answer. The answer is 1 x-value per graph. Every point on the graph will have
\n" ); document.write( "the same value of x. For the first problem, you are told that the point on the graph is
\n" ); document.write( "the coordinate pair (2, -4). This means that it must have an x value of +2, and therefore,
\n" ); document.write( "every point on the vertical graph must have an x-value of +2 to ensure that the point (2, -4)
\n" ); document.write( "will be on the graph as well as lots of other points ... all having 2 for their
\n" ); document.write( "x-value. As examples ... all the following points are on the graph for the first problem:
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\n" ); document.write( "(2,10); (2,5); (2,0); (2, -4); (2,-5); (2,-10) ... and so on.
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\n" ); document.write( "Similarly, for the second problem you are told that the point (-4, 7) must be on the graph.
\n" ); document.write( "Therefore, you can say that the to be perpendicular to the x-axis, every point on this
\n" ); document.write( "graph must have an x-value of -4.
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\n" ); document.write( "To help you see this, the graphs you are looking for as the answers are shown below. You
\n" ); document.write( "should convince yourself that they are perpendicular to the x-axis and parallel to the y-axis.
\n" ); document.write( "The \"red\" graph is the answer for the first problem [through the point (2,-4)] and the
\n" ); document.write( "\"green\" graph is the answer for the second problem [through the point (-4,7)]. You should
\n" ); document.write( "find the point (2,-4) and convince yourself that it is on the red graph. And you should also
\n" ); document.write( "find the point (-4,7) and convince yourself that it is on the green graph.
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\n" ); document.write( "Hope this helps you to understand the problem.
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