document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171592>Question 1171592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help writing an equation for this graph please.\r<BR>\n" );
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document.write( "https://imgur.com/a/bKYs8v2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796483 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=796483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The two blue points indicated on the line are (0,-4) and (3,-7). You can pick any two points on the blue line, but I'll pick these two as they stand out more.\r<BR>\n" );
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document.write( "Use the slope formula to get<BR>\n" );
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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-7-%28-4%29%29%2F%283-0%29 ALIGN=MIDDLE  ALT=\"m+=+%28-7-%28-4%29%29%2F%283-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > note how we subtract the y values up top, and subtract the x values in the same order down below\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-7%2B4%29%2F%283-0%29 ALIGN=MIDDLE  ALT=\"m+=+%28-7%2B4%29%2F%283-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-3%29%2F%283%29 ALIGN=MIDDLE  ALT=\"m+=+%28-3%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-1 ALIGN=MIDDLE  ALT=\"m+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The slope is -1.\r<BR>\n" );
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document.write( "A slope of -1 means each time we move down 1, we move to the right 1.<BR>\n" );
document.write( "We could say<BR>\n" );
document.write( "slope = rise/run = -1/1<BR>\n" );
document.write( "to be more thorough\r<BR>\n" );
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document.write( "rise = -1 means we move down 1<BR>\n" );
document.write( "run = 1 means we move to the right 1\r<BR>\n" );
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document.write( "The y intercept is where the graph crosses the y axis. Visually this is shown as (0,-4) so b = -4 is the y intercept.\r<BR>\n" );
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document.write( "If we didn't have this point, we could plug either point into y = mx+b, along with the slope we just found, to solve for b.\r<BR>\n" );
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document.write( "So if we tried (x,y) = (0,-4) and m = -1, then,<BR>\n" );
document.write( "y = mx+b<BR>\n" );
document.write( "-4 = (-1)(0)+b<BR>\n" );
document.write( "-4 = 0+b<BR>\n" );
document.write( "-4 = b<BR>\n" );
document.write( "b = -4\r<BR>\n" );
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document.write( "or we could try (x,y) = (3,-7) and m = -1<BR>\n" );
document.write( "y = mx+b<BR>\n" );
document.write( "-7 = (-1)*(3)+b<BR>\n" );
document.write( "-7 = -3+b<BR>\n" );
document.write( "-7 = b-3<BR>\n" );
document.write( "b-3 = -7<BR>\n" );
document.write( "b-3+3 = -7+3 ... adding 3 to both sides<BR>\n" );
document.write( "b = -4\r<BR>\n" );
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document.write( "Either way we get the same y intercept value.\r<BR>\n" );
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document.write( "To wrap things up, we found<BR>\n" );
document.write( "m = -1 = slope<BR>\n" );
document.write( "b = -4 = y intercept\r<BR>\n" );
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document.write( "Therefore, we go from<BR>\n" );
document.write( "y = mx+b<BR>\n" );
document.write( "to<BR>\n" );
document.write( "y = -1x+(-4)\r<BR>\n" );
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document.write( "This can be simplified to y = -x-4\r<BR>\n" );
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document.write( "As a way to check, plug in x = 0 and you should get y = -4. This is the point (0,-4). Also, plugging in x = 3 should lead to y = -7. This is the point (3,-7).\r<BR>\n" );
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document.write( "Answer:  y = -x-4\r<BR>\n" );
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