document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=228442>Question 228442</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the line L has a slope of (-3/5) and passes through the points (11, t) and (2t, -8 ). Find the equation of L and its x and y intercepts. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #169569 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=169569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose the line L has a slope of (-3/5) and passes through the points (11, t) and (2t, -8 ). Find the equation of L and its x and y intercepts.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 1.  The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept b at x=0 or point (0,b).  Here, the slope m=-3/5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 2.  The slope 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( "Step 3.  Let (x1,y1)=(11,t) or x1=11 and y1=t and (x2,y2)=(2t,-8) or x2=2t and y2=-8.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 4.  Now we're given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-3%2F5 ALIGN=MIDDLE  ALT=\"m=-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Substituting above values and variables in the slope equation m yields the following steps:\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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F5=%28-8-t%29%2F%282t-11%29 ALIGN=MIDDLE  ALT=\"-3%2F5=%28-8-t%29%2F%282t-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 5.  Multiply 5(2t-11) to both sides to get rid of denominators on both sides of 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=5%282t-11%29%2A%28-3%2F5%29=5%282t-11%29%28-8-t%29%2F%282t-11%29 ALIGN=MIDDLE  ALT=\"5%282t-11%29%2A%28-3%2F5%29=5%282t-11%29%28-8-t%29%2F%282t-11%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=-3%282t-11%29=5%28-8-t%29 ALIGN=MIDDLE  ALT=\"-3%282t-11%29=5%28-8-t%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=-6t%2B33=-40-5t ALIGN=MIDDLE  ALT=\"-6t%2B33=-40-5t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Add 6t+40 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=-6t%2B33%2B6t%2B40=-40-5t%2B6t%2B40 ALIGN=MIDDLE  ALT=\"-6t%2B33%2B6t%2B40=-40-5t%2B6t%2B40\"   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=73=t ALIGN=MIDDLE  ALT=\"73=t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 6.  Therefore the points are (x1,y1)=(11,73) and (x2,y2)=(2*73,-8) or (x2,y2)=(146,-8)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's double check the slope m=-3/5 with these two points (11,73) and (146,-8).\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=%28-8-73%29%2F%28146-11%29=-81%2F135=-3%2F5 ALIGN=MIDDLE  ALT=\"m=%28-8-73%29%2F%28146-11%29=-81%2F135=-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > so it works.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 7.  Now to get our linear equation,  we choose one of the points say (11,73) and the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-3%2F5 ALIGN=MIDDLE  ALT=\"m=-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  We have (x1,y1)=(11,73) or x1=11 and y1=73.  Let other point be (x2,y2)=(x,y) or x2=x and y2=y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 8.  Now we're given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-3%2F5 ALIGN=MIDDLE  ALT=\"m=-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Substituting above values and variables in the slope equation m yields the following steps to get a linear 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=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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F5=%28y-73%29%2F%28x-11%29 ALIGN=MIDDLE  ALT=\"-3%2F5=%28y-73%29%2F%28x-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply by (x-11) 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=-3%28x-11%29%2F5=y-73 ALIGN=MIDDLE  ALT=\"-3%28x-11%29%2F5=y-73\"   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=-3x%2F5%2B33%2F5=y-73 ALIGN=MIDDLE  ALT=\"-3x%2F5%2B33%2F5=y-73\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Add 73 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=-3x%2F5%2B33%2F5%2B73=y-73%2B73 ALIGN=MIDDLE  ALT=\"-3x%2F5%2B33%2F5%2B73=y-73%2B73\"   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=-3x%2F5%2B33%2F5%2B365%2F5=y ALIGN=MIDDLE  ALT=\"-3x%2F5%2B33%2F5%2B365%2F5=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=-3x%2F5%2B398%2F5=y ALIGN=MIDDLE  ALT=\"-3x%2F5%2B398%2F5=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 9.  Let's see if the other point (146,-8) satisfies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%2F5%2B398%2F5 ALIGN=MIDDLE  ALT=\"y=-3x%2F5%2B398%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a check\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8=-3%2A146%2F5%2B398%2F5 ALIGN=MIDDLE  ALT=\"-8=-3%2A146%2F5%2B398%2F5\"   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=-8=-438%2F5%2B398%2F5=-40%2F5 ALIGN=MIDDLE  ALT=\"-8=-438%2F5%2B398%2F5=-40%2F5\"   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=-8=-8 ALIGN=MIDDLE  ALT=\"-8=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  which is a true statement\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 10.  The equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%2F5%2B398%2F5 ALIGN=MIDDLE  ALT=\"y=-3x%2F5%2B398%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 11.  The x-intercept is when y=0 or\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-3x%2F5%2B398%2F5 ALIGN=MIDDLE  ALT=\"0=-3x%2F5%2B398%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > after add 3x/5 and multiplying by 5 to both sides of the equation we have\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=398 ALIGN=MIDDLE  ALT=\"3x=398\"   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=x=398%2F3 ALIGN=MIDDLE  ALT=\"x=398%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ANSWER to finding the x-intercept.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 12.  The y-intercept is when x=0 or\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=-3%2A0%2F5%2B398%2F5 ALIGN=MIDDLE  ALT=\"y=-3%2A0%2F5%2B398%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > after add 3x/5 and multiplying by 5 to both sides of the equation we have\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=398%2F5 ALIGN=MIDDLE  ALT=\"y=398%2F5\"   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=398%2F5 ALIGN=MIDDLE  ALT=\"y=398%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ANSWER to finding the y-intercept.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 13.  ANSWER:  The equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%2F5%2B398%2F5 ALIGN=MIDDLE  ALT=\"y=-3x%2F5%2B398%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The x-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=398%2F3 ALIGN=MIDDLE  ALT=\"a=398%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or at point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=398%2F3 ALIGN=MIDDLE  ALT=\"398%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >).  The y-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=398%2F5 ALIGN=MIDDLE  ALT=\"b=398%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or at point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=398%2F5 ALIGN=MIDDLE  ALT=\"398%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I hope the above steps were helpful.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Good luck in your studies!\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" );