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2x - y = 4
\n" ); document.write( "2x - y = 6
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\n" ); document.write( "Let's put these equations into the slope intercept form of y = mx + b where m is the slope
\n" ); document.write( "of the graph and b is the point where the graph crosses the y-axis.
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\n" ); document.write( "The first equation can be put into slope intercept form in two steps. First subtract
\n" ); document.write( "2x from both sides of the equation to get -y = -2x + 4. Then multiply the entire equation
\n" ); document.write( "by -1 to get the slope intercept form of y = 2x -4. This tells you that the graph crosses the
\n" ); document.write( "y-axis at -4, a point designated by (0, -4). You can easily get another point on the graph
\n" ); document.write( "by returning to the original equation and setting y equal to zero. This reduces the
\n" ); document.write( "equation to 2x = 4 which after dividing both sides by 2 becomes x = 2. So the point
\n" ); document.write( "(2, 0) is also on the graph. You can plot the two points (0, -4) and (2, 0) and draw a line
\n" ); document.write( "through them to see what the graph looks like. And you also know the slope of the line
\n" ); document.write( "is +2 because in the slope intercept form that is the multiplier of the x term.
\n" ); document.write( ".
\n" ); document.write( "You can do a similar analysis for the second equation. Put it into slope intercept
\n" ); document.write( "form. Do that by subtracting 2x from both sides to get -y = -2x + 6. Multiply this entire
\n" ); document.write( "equation by -1 to get the slope intercept form of y = 2x - 6. This tells you that the graph
\n" ); document.write( "has a slope of +2 and crosses the y-axis at -6. And a y-axis crossing at -6 can be written
\n" ); document.write( "as the point (0, -6). You can again find another point on the graph by returning to the
\n" ); document.write( "original equation and setting y equal to zero. When you do the equation reduces to
\n" ); document.write( "2x = 6 and dividing by 2 determines that x = 3. So the point (3, 0) is also on this graph.
\n" ); document.write( "Plot the points (0, -6) and (3,0) and draw a line through them.
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\n" ); document.write( "You should now see from the graphs that the lines look parallel. In fact, they have to
\n" ); document.write( "be parallel because they both have the same slope of +2, the difference being that one
\n" ); document.write( "graph crosses the y-axis at -4 and the other at -6.
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\n" ); document.write( "The thing that is critical is that parallel lines never cross. And a crossing point of
\n" ); document.write( "linear graphs is the common solution for the system. Therefore, this given set of equations
\n" ); document.write( "has no common solution ... trick question.
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\n" ); document.write( "Hopefully this helps to give you a little more understanding of graphing linear equations
\n" ); document.write( "and associating the equations with the graphs. \n" ); document.write( "