document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=224721>Question 224721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use patterns or a linear equation to complete the table.\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "x         y\r<BR>\n" );
document.write( "\n" );
document.write( "1       <BR>\n" );
document.write( "-1\r<BR>\n" );
document.write( "\n" );
document.write( "3         3\r<BR>\n" );
document.write( "\n" );
document.write( "5         7\r<BR>\n" );
document.write( "\n" );
document.write( "10       ?\r<BR>\n" );
document.write( "\n" );
document.write( "50       ?\r<BR>\n" );
document.write( "\n" );
document.write( "100    ?\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167839 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=167839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use patterns or a linear equation to complete the table.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Based on the Steps below the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-3 ALIGN=MIDDLE  ALT=\"y=2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "x         y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1       y=2(1)-3=-1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-1     y=2(-1)-3=-5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3         3  use this point to find slope and equation of line  (see below)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5         7  use this point to find slope and equation of line  (see below)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "10       ?  y=2(10)-3=17\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "50       ?  y=2(50)-3=100-3=97\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 1.  We are going to find the equation for this line in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point(0,b).  Once we have this equation we can get the rest of the points.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 2.  Based on your problem we will use two points to draw a line and these points are (3,3) and (5,7)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 3.  The slope of the line m is given as\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "where for our example is x1=3, y1=3, x2=5 and y2=7 (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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 4.  Substituting the above values in the slope equation gives\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%287-3%29%2F%285-3%29 ALIGN=MIDDLE  ALT=\"m=%287-3%29%2F%285-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=4%2F2 ALIGN=MIDDLE  ALT=\"m=4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2 ALIGN=MIDDLE  ALT=\"m=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 5.  The slope is calculated as 2 or m=-2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 6.  Now use the slope equation of step 1 and choose one of the given points.  I'll choose point (3,3).   Letting y=y2 and x=x2 and substituting m=2 in the slope equation given as,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2=%28y-3%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"+2=%28y-3%29%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2=%28y-3%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"+2=%28y-3%29%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 7.  Multiply both sides of equation by x-3 to get rid of denomination found on the right side of the equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%28x-3%29=%28x-3%29%28y-3%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"+2%28x-3%29=%28x-3%29%28y-3%29%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%28x-3%29=y-3 ALIGN=MIDDLE  ALT=\"+2%28x-3%29=y-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 8.  Now simplify and put the above equation into slope-intercept form.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-6=y-3 ALIGN=MIDDLE  ALT=\"2x-6=y-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Add 3 to both sides of the equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-6%2B3=y-3%2B3 ALIGN=MIDDLE  ALT=\"2x-6%2B3=y-3%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3=y ALIGN=MIDDLE  ALT=\"2x-3=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-3 ALIGN=MIDDLE  ALT=\"y=2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in in slope-intercept form where m=2 and y-intercept=-3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 9.  See if the other point (5,7) or x=5 and y=7 satisfies this equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2Ax-3 ALIGN=MIDDLE  ALT=\"y=2%2Ax-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7=2%2A5-3 ALIGN=MIDDLE  ALT=\"7=2%2A5-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7=7 ALIGN=MIDDLE  ALT=\"7=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  So the point (5,7) satisfies the equation and is on the line.  In other words, you can use the other point to check your work.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note the  above equation can be also be transform into standard form as\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2By=-3 ALIGN=MIDDLE  ALT=\"-2x%2By=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "See graph below to check the above steps.\r<BR>\n" );
document.write( "<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=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=-2+x+%2B+1+y+=+-3 ALIGN=MIDDLE  ALT=\"-2+x+%2B+1+y+=+-3\"   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+=+--2%2F1 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+--2%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. -3/-2 = 1.5.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -3/1 = -3.</LI><LI>Slope is --2/1 = 2.</LI><LI> Equation in slope-intercept form: y=2*x+-3.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+1.5-8%2C+1.5%2B8%2C+-3-8%2C+-3%2B8%2C+2%2Ax%2B-3+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+1.5-8%2C+1.5%2B8%2C+-3-8%2C+-3%2B8%2C+2%2Ax%2B-3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
document.write( "</TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I hope the above steps were helpful. \r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "And good luck in your studies!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );