document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73680>Question 73680</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132191415/algebrahomeworkh>college algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I need to know if I have done these right!! Thank you so much!!\r<BR>\n" );
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document.write( ")  Given a line containing the points (1,3), (2,4), (3,5) determine the slope-intercept form of the equation, give one additional point on this line and graph the function. \r<BR>\n" );
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document.write( "Show your work here:  y2-y1/x2-x1= -4,-6  \r<BR>\n" );
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document.write( "Give one additional point in (x,y) form that would fall on this line: 4,6\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53188 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=53188\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm sorry it took so long for me to get to your problem.<BR>\n" );
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document.write( "The slope-intercept form of an equation is:<BR>\n" );
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document.write( "y = mx + b<BR>\n" );
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document.write( "where m, the multiplier of x, is the slope of the graph, and b is the point on the y-axis where<BR>\n" );
document.write( "the graph crosses.<BR>\n" );
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document.write( "So let's find the slope. You have the equation correct for finding the slope. That equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We know that all three of the given points are on the line.  All we have to do is identify<BR>\n" );
document.write( "one of the points as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B2%5Dy%5B2%5D%29 ALIGN=MIDDLE  ALT=\"%28x%5B2%5Dy%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and another of the points as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B1%5D+y%5B1%5D%29 ALIGN=MIDDLE  ALT=\"%28x%5B1%5D+y%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "It's a little easier to see if we choose as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B2%5D+y%5B2%5D%29 ALIGN=MIDDLE  ALT=\"%28x%5B2%5D+y%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > a point that is to<BR>\n" );
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document.write( "the right of the point we call <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B1%5Dy%5B1%5D%29 ALIGN=MIDDLE  ALT=\"%28x%5B1%5Dy%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. It doesn't have to be that way because it <BR>\n" );
document.write( "will work out the same no matter what.<BR>\n" );
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document.write( "Anyhow let's choose as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B2%5D+y%5B2%5D%29 ALIGN=MIDDLE  ALT=\"%28x%5B2%5D+y%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the point  (3,5). By comparison, that means<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+3 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+5 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Now let's choose as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B1%5D+y%5B1%5D%29 ALIGN=MIDDLE  ALT=\"%28x%5B1%5D+y%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the point (1,3).  By comparison of these two <BR>\n" );
document.write( "that means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+1 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+3 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
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document.write( "Then all we do to calculate the slope is to substitute these 4 values into the slope equation<BR>\n" );
document.write( "as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%285+-+3%29%2F%283+-+1%29+=+%282%2F2%29+=+1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So we have the slope of m = 1.  Plug that value of m into the slope intercept form of the<BR>\n" );
document.write( "equation and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+mx%2B+b+=1%2Ax+%2Bb+=+x+%2B+b ALIGN=MIDDLE  ALT=\"+y+=+mx%2B+b+=1%2Ax+%2Bb+=+x+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "To solve for b, all we need to do is to take one of the given points and plug its x and y<BR>\n" );
document.write( "values into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x+%2B+b ALIGN=MIDDLE  ALT=\"+y+=+x+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Then we can solve for b.  For example,<BR>\n" );
document.write( "let's take the point (1,3) that we were given.  Plug 1 in for x and 3 in for y and the<BR>\n" );
document.write( "slope intercept equation becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+1+%2B+b ALIGN=MIDDLE  ALT=\"3+=+1+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Solve this by subtracting 1 from both<BR>\n" );
document.write( "sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+b ALIGN=MIDDLE  ALT=\"2+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then take this value for b and plug it into the slope intercept form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x+%2B+b ALIGN=MIDDLE  ALT=\"y+=+x+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "you have the final version of the slope intercept form as being:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x+%2B+2 ALIGN=MIDDLE  ALT=\"y+=+x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next you said that you thought the point (4,6) was on the graph. Let's check that out by<BR>\n" );
document.write( "putting 4 into our slope intercept equation for x and 6 in for y and see if the equation<BR>\n" );
document.write( "is still true.  When we do the substitution we get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+4+%2B+2 ALIGN=MIDDLE  ALT=\"6+=+4+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Well, that certainly is true, so your point of (4,6) IS on the graph.<BR>\n" );
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document.write( "Hope this helps you to understand the first part of the problem a little better. </SPAN>\n" );
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