document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=281373>Question 281373</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the line thru (1,1) wiht a slope of 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #204386 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=204386\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The slope of 3 means that for a change of 1 'x' there will be a change of 3 'y'.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "m = rise/run = 3/1<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We have the point (1,1), so the next point would be (2,4). With two points, you can graph a straight line.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Or we can address the problem in terms of  y = mx + b, which is the slope-intercept form of an equation.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "y = 3x + b<BR>\n" );
document.write( ".<BR>\n" );
document.write( "But then the question is, \"What is the value 'b' to be sure it goes through the point (1,1)?\"<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Well, (1,1) means that when x=1, y =1, so we can show this as:<BR>\n" );
document.write( "1 = 3(1) + b<BR>\n" );
document.write( "b = -2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "This suggests the equation of the line with slope = 3 that goes through the point (1,1) is:<BR>\n" );
document.write( "y = 3x -2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Graphing it we can see...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-5%2C5%2C-5%2C5%2C3%2Ax-2%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-5%2C5%2C-5%2C5%2C3%2Ax-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "That looks correct.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We also can do additional checking.<BR>\n" );
document.write( "Some other points of interest are the y-intercept and the x-intercept.<BR>\n" );
document.write( "The y-intercept is where x=0.<BR>\n" );
document.write( "y = 3(0)-2 = -2<BR>\n" );
document.write( "(0, -2)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The x-intercept is where y=0.<BR>\n" );
document.write( "0 = 3x -2<BR>\n" );
document.write( "x = 2/3<BR>\n" );
document.write( "(2/3, 0)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "By inspecting the graph, you can see these points are on the line, too.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Done </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );