document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120173>Question 120173</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977223/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find the slope of each line. If the line has no slope, say so. \r<BR>\n" );
document.write( "\n" );
document.write( "y = 3x-2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88053 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=88053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope_intercept ALIGN=MIDDLE  ALT=\"slope_intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" >  form of a linear equation is : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B+b ALIGN=MIDDLE  ALT=\"y+=+mx+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >...where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents a slope, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >represents <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y_intercept ALIGN=MIDDLE  ALT=\"y_intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" >(or the point where the line crosses y axis)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3x-2 ALIGN=MIDDLE  ALT=\"y+=+3x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...if you compare this equation to the standard form, you see what <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > are...this is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope_intercept ALIGN=MIDDLE  ALT=\"slope_intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" > form\r<BR>\n" );
document.write( "\n" );
document.write( "slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+3 ALIGN=MIDDLE  ALT=\"m+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (rise/run=3)\r<BR>\n" );
document.write( "\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-2 ALIGN=MIDDLE  ALT=\"b+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....the line crosses <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > axis at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "here is detailed explanation with a graph:\r<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=graphing_linear_equations.solver>Graphing Linear Equations</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>In order to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2Ax-2 ALIGN=MIDDLE  ALT=\"y=3%2Ax-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > we only need to plug in two points to draw the line<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So lets plug in some points<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plug in x=-2<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2A%28-2%29-2 ALIGN=MIDDLE  ALT=\"y=3%2A%28-2%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-6-2 ALIGN=MIDDLE  ALT=\"y=-6-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8 ALIGN=MIDDLE  ALT=\"y=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So here's one point (-2,-8)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-12%2C9%2C+-18%2C+5%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-2%2C-8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C-8%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now lets find another point <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plug in x=-1<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2A%28-1%29-2 ALIGN=MIDDLE  ALT=\"y=3%2A%28-1%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3-2 ALIGN=MIDDLE  ALT=\"y=-3-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5 ALIGN=MIDDLE  ALT=\"y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So here's another point (-1,-5). Add this to our graph<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-12%2C9%2C+-18%2C+5%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-1%2C-5%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-1%2C-5%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-2%2C-8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C-8%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now draw a line through these points<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-12%2C9%2C+-18%2C+5%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-12-10%2C3%2A%28-12-10%29%2B-2%2C9%2B10%2C3%2A%289%2B10%29%2B-2%29%2C%0D%0A++++blue%28+circle%28+-1%2C-5%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-1%2C-5%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-2%2C-8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C-8%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > So this is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2Ax-2 ALIGN=MIDDLE  ALT=\"y=3%2Ax-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (-2,-8) and (-1,-5)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So from the graph we can see that the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F1 ALIGN=MIDDLE  ALT=\"3%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which tells us that in order to go from point to point we have to start at one point and go  up 3 units and to the right 1 units to get to the next point) the y-intercept is (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)and the x-intercept is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.666666666666667 ALIGN=MIDDLE  ALT=\"0.666666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0)  ,or (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0) <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  We could graph this equation another way. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-2 ALIGN=MIDDLE  ALT=\"b=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >). <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So we have one point (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C11%2C+-12%2C+11%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14-0.05%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now since the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F1 ALIGN=MIDDLE  ALT=\"3%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that in order to go from point to point we can use the slope to do so. So starting at (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we can go up 3 units <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28++600%2C+600%2C+-10%2C11%2C+-12%2C+11%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14-0.05%29+%29%0D%0A++blue%28+arc%28+0%2C+-2%2B%283%2F2%29%2C+2%2C+3%2C+90%2C+270+%29+%29%0D%0A++%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  and to the right 1 units to get to our next point<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28++600%2C+600%2C+-10%2C11%2C+-12%2C+11%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+1%2C1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+1%2C1%2C+0.14-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-2%2B%283%2F2%29%2C+2%2C+3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%281%2F2%29%2C+1%2C+1%2C+2%2C+180%2C+360+%29+%29%0D%0A++%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Now draw a line through those points to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2Ax-2 ALIGN=MIDDLE  ALT=\"y=3%2Ax-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C11%2C+-12%2C+11%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C3%2A%28-10-10%29%2B-2%2C11%2B10%2C3%2A%2811%2B10%29%2B-2%29%2C%0D%0A++++blue%28+circle%28+1%2C1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+1%2C1%2C+0.14-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-2%2C+0.14-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-2%2B%283%2F2%29%2C+2%2C+3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%281%2F2%29%2C+1%2C+1%2C+2%2C+180%2C+360+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > So this is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2Ax-2 ALIGN=MIDDLE  ALT=\"y=3%2Ax-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (0,-2) and (1,1)<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );