document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=215585>Question 215585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the y intercept of the points (1, 202) and (4, 382)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162893 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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/cgi-bin/show-face.mpl?user=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=162893\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the y intercept of the points (1, 202) and (4, 382)?\r<BR>\n" );
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document.write( "Step 1.  We need to find an equation in slope intercept form given as y=mx+b where m is the slope and b is the y-intercept at point (0,b).\r<BR>\n" );
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document.write( "Step 2.  The slope of the line m is given as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m=%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"+m=%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where for our example is x1=1, y1=202, x2=4 and y2=382 (think of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope=rise%2Frun ALIGN=MIDDLE  ALT=\"slope=rise%2Frun\"   DISABLED_style= \"max-width:90%; height:auto;\" >).  You can choose the points the other way around but be consistent with the x and y coordinates.  You will get the same result.\r<BR>\n" );
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document.write( "Step 3.  Substituting the above values in the slope equation gives\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28382-202%29%2F%284-1%29 ALIGN=MIDDLE  ALT=\"m=%28382-202%29%2F%284-1%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=180%2F3 ALIGN=MIDDLE  ALT=\"m=180%2F3\"   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=60 ALIGN=MIDDLE  ALT=\"m=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4.  The slope is calculated as 60 or m=60.\r<BR>\n" );
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document.write( "Step 5.  Now use the slope equation of step 1 and choose one of the given points.  I'll choose point (1,202).   Letting y=y2 and x=x2 and substituting m=60 in the slope equation given as,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m=%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"+m=%28y2-y1%29%2F%28x2-x1%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=+60=%28y-202%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"+60=%28y-202%29%2F%28x-1%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=+60=%28y-202%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"+60=%28y-202%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6.  Multiply both sides of equation by x-1 to get rid of denomination found on the right side of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+60%28x-1%29=%28x-1%29%28y-202%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"+60%28x-1%29=%28x-1%29%28y-202%29%2F%28x-1%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=+60x-60=y-202 ALIGN=MIDDLE  ALT=\"+60x-60=y-202\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 7.  Now simplify and put the above equation into slope-intercept form.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60x-60=y-202 ALIGN=MIDDLE  ALT=\"60x-60=y-202\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 202 to both sides of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60x-60%2B202=y-202%2B202 ALIGN=MIDDLE  ALT=\"60x-60%2B202=y-202%2B202\"   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=60x%2B142=y ALIGN=MIDDLE  ALT=\"60x%2B142=y\"   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=y=60x%2B142 ALIGN=MIDDLE  ALT=\"y=60x%2B142\"   DISABLED_style= \"max-width:90%; height:auto;\" >   ANSWER in slope-intercept form.  m=60 and y-intercept=142\r<BR>\n" );
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document.write( "Step 8.  See if the other point (4, 382) or x=4 and y=382 satisfies this equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=60x%2B142 ALIGN=MIDDLE  ALT=\"y=60x%2B142\"   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=382=60%2A4%2B142 ALIGN=MIDDLE  ALT=\"382=60%2A4%2B142\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "{{382=382}}}  So the point (4,382) satisfies the equation and is on the line.  In other words, you can use the other point to check your work.\r<BR>\n" );
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document.write( "Note: above equation can be also be transform into standard form as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-60x%2By=142 ALIGN=MIDDLE  ALT=\"-60x%2By=142\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "See graph below to check the above steps.\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-60+x+%2B+1+y+=+142 ALIGN=MIDDLE  ALT=\"-60+x+%2B+1+y+=+142\"   DISABLED_style= \"max-width:90%; height:auto;\" > describes a sloping line. For any <BR>\n" );
document.write( "  equation ax+by+c = 0, slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Fb+=+--60%2F1 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+--60%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<UL><LI>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. 142/-60 = -2.36666666666667.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 142/1 = 142.</LI><LI>Slope is --60/1 = 60.</LI><LI> Equation in slope-intercept form: y=60*x+142.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-2.36666666666667-8%2C+-2.36666666666667%2B8%2C+142-8%2C+142%2B8%2C+60%2Ax%2B142+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
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document.write( "I hope the above steps were helpful. \r<BR>\n" );
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document.write( "And good luck in your studies!\r<BR>\n" );
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document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J<BR>\n" );
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