document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201391>Question 201391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write an equation in standard form for a line passing through the pair of points.\r<BR>\n" );
document.write( "\n" );
document.write( "(-2,0) and (4,-5)\r<BR>\n" );
document.write( "\n" );
document.write( "possible answers:<BR>\n" );
document.write( "2x-9y=-37<BR>\n" );
document.write( "-5x-6y=10<BR>\n" );
document.write( "-2x+9y=-37<BR>\n" );
document.write( "5x-6y=10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #151618 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrapro18><B>algebrapro18(249)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrapro18><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=151618\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> write an equation in standard form for a line passing through the pair of points. (-2,0) and (4,-5).<br>\r<BR>\n" );
document.write( "\n" );
document.write( "Well from the points given we know that:<br>\r<BR>\n" );
document.write( "\n" );
document.write( "x1 = -2, y1= 0, x2 = 4, y2 = -5<br>\r<BR>\n" );
document.write( "\n" );
document.write( "First we need to find the slope of the line between those two points:<BR>\n" );
document.write( "That uses the formula: m = y2-y1/x2-x1<br>\r<BR>\n" );
document.write( "\n" );
document.write( "So from above we get that: m = (-5-0)/ (4--2) = -5/6.<br>\r<BR>\n" );
document.write( "\n" );
document.write( "Now we can continue in 1 of two ways. Either we can plug in to the slope-intercept form and solve for b and then get into standard form, or we can use the point slope formula and get it in standard form.<br>\r<BR>\n" );
document.write( "\n" );
document.write( "Option 1: slope-intercept form:<br>\r<BR>\n" );
document.write( "\n" );
document.write( "we know that y = mx+b and we have a y, x, and m so we can solve for b.<br>\r<BR>\n" );
document.write( "\n" );
document.write( "y = mx+b                        <BR>\n" );
document.write( "0 = -5/6(-2)+b                 <BR>\n" );
document.write( "0 = 5/3+b                       <BR>\n" );
document.write( "b = -5/3<br>                       \r<BR>\n" );
document.write( "\n" );
document.write( "or<br>\r<BR>\n" );
document.write( "\n" );
document.write( "y = mx+b<BR>\n" );
document.write( "-5 = (-5/6)(4)+b<BR>\n" );
document.write( "-5 = -10/3 + b<BR>\n" );
document.write( "-5/3 = b<br>\r<BR>\n" );
document.write( "\n" );
document.write( "so now we know that y = -5/6x-5/3.  To get it into standard form we need to get the x and the y isolated on the same side.  <br>\r<BR>\n" );
document.write( "\n" );
document.write( "y = -5/6x-5/3<BR>\n" );
document.write( "6y = -5x - 10<BR>\n" );
document.write( "5x + 6y = -10 <BR>\n" );
document.write( "-(5x+6y) = 10<BR>\n" );
document.write( "-5x-6y = 10<br>\r<BR>\n" );
document.write( "\n" );
document.write( "Option 2: Point-Slope form<BR>\n" );
document.write( "We know that y-y1=m(x-x1) so now we just plug in and simplify(not solve).<br>\r<BR>\n" );
document.write( "\n" );
document.write( "y - 0 = -5/6(x--2)<BR>\n" );
document.write( "y = -5/6(x+2)<BR>\n" );
document.write( "y = -5/6x-5/3<br>\r<BR>\n" );
document.write( "\n" );
document.write( "and now we just need to get into standard form.<br>\r<BR>\n" );
document.write( "\n" );
document.write( "y = -5/6x-5/3<BR>\n" );
document.write( "6y = -5x - 10<BR>\n" );
document.write( "5x + 6y = -10 <BR>\n" );
document.write( "-(5x+6y) = 10<BR>\n" );
document.write( "-5x-6y = 10<br>\r<BR>\n" );
document.write( "\n" );
document.write( "Now I will leave it to you to check our answer, and you will see its right. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );