document.write( "Question 934439: what does the \"\" mean? What do I have to do on the graph paper?\r
\n" ); document.write( "\n" ); document.write( "Using a scale of 2cm to 1 unit on the x and y axis, draw the graph of y = 2x+1 and x-3y= 2 for \"-2\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #567636 by KMST(5328) $\"\"$ $\"About$

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It seems like the paper has to be
\n" ); document.write( "either graph paper somehow having squares measuring 2 cm,
\n" ); document.write( "or plain paper without lines.
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\n" ); document.write( "One interpretation of the $\"-2%3Cx%3C5\"$ would be
\n" ); document.write( "that you have to show the graph of $\"y=2x%2B1\"$ from point (-2,-3) to point (5,11) ,
\n" ); document.write( "but that would make the graph 28 cm tall.
\n" ); document.write( "
\n" ); document.write( "The $\"-2%3Cx%3C5\"$ must just mean that your scale on the x-axis should go from -2 to 5.
\n" ); document.write( "There is no instruction for the y-axis scale,
\n" ); document.write( "but -2 to 5 works well too (see below).
\n" ); document.write( " $\"graph%28300%2C300%2C-2%2C5%2C-2%2C5%2C2x%2B1%2Cx%2F3-2%2F3%29\"$
\n" ); document.write( "Since the scale is 2 cm to 1 unit,
\n" ); document.write( "the distance between marks on each axis would be 2 cm,
\n" ); document.write( "and the graph above would measure 14 cm by 14 cm.
\n" ); document.write( "To plot each line you would need 2 points, or a point and the slope.
\n" ); document.write( " $\"y=2x%2B1\"$ is an equation in slope-intercept form,
\n" ); document.write( "which makes it clear that the line has a slope of $\"2\"$ ,
\n" ); document.write( "and a y-intercept of $\"1\"$ , so (0,1) is one point,
\n" ); document.write( "and for every 1 unit increase in x, y increases by 2,
\n" ); document.write( "so with those increases, from (0,1) we get to (1,3),
\n" ); document.write( "and then to (2,5).
\n" ); document.write( "To graph $\"y=2x%2B1\"$ , you could plot points (0,1) and (2,5),
\n" ); document.write( "and draw the line that passes through them.
\n" ); document.write( " $\"x-3y=2\"$ is given in standard form,
\n" ); document.write( "so graphing it is not that easy.
\n" ); document.write( "You notice that for $\"y=0\"$ $\"x=2\"$ ,
\n" ); document.write( "so the line passes through (2,0).
\n" ); document.write( "The slope is $\"1%2F3\"$ ,
\n" ); document.write( "so for every 3 units increase in x,
\n" ); document.write( "there is a 1 unit increase in y.
\n" ); document.write( "Using those increments, staring from (2,0), we get to (5,1),
\n" ); document.write( "so to graph $\"x-3y=2\"$ you could points (2,0) and (5,1),
\n" ); document.write( "and draw the line that passes through them.
\n" ); document.write( "The lines seem to intersect at (-1,-1),
\n" ); document.write( "If you substitute $\"x=-1\"$ and $\"x=-1\"$ into the equations of both lines,
\n" ); document.write( "it makes the equations true.
\n" ); document.write( "That means that point (-1,-1) belongs to both lines,
\n" ); document.write( "so it is the intersection point,
\n" ); document.write( "and the solution to the system of equations
\n" ); document.write( " $\"system%28y=2x%2B1%2Cx-3y=2%29\"$ ,
\n" ); document.write( "which you have solved by graphing.
\n" ); document.write( "That was the point of the exercise.
\n" ); document.write( "Without the request to graph for $\"-2%3Cx%3C5\"$ ,
\n" ); document.write( "you could have made this graph:
\n" ); document.write( " $\"graph%28300%2C300%2C-0.5%2C9.5%2C-0.5%2C9.5%2C2x%2B1%2Cx%2F3-2%2F3%29\"$ ,
\n" ); document.write( "which does not show the intersection point. \n" ); document.write( "

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