document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112005>Question 1112005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Given the linear equation : -3x + 5y = 15<BR>\n" );
document.write( "          a. Show and explain the process to find the x and y intercepts<BR>\n" );
document.write( "          b. Use the x- and y-intercepts found in part a and the slope formula to find the slope. Show all work.<BR>\n" );
document.write( "          c. Begin with the form -3x+5y=15 and write the equation in slope intercept form. Show all work.<BR>\n" );
document.write( "          d. Based on the slope-intercept form of the line, what are the slope and y-intercept ? Are these values consistent with answers in parts a and b ?<BR>\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 #727040 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=727040\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. <BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x+=+15 ALIGN=MIDDLE  ALT=\"-3x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and solving for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > we find<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%2F%28-3%29 ALIGN=MIDDLE  ALT=\"x=15%2F%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=highlight%28-5%29 ALIGN=MIDDLE  ALT=\"x=highlight%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the x-intercept.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+=+15 ALIGN=MIDDLE  ALT=\"5y+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and solving for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > we find<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=15%2F5 ALIGN=MIDDLE  ALT=\"5=15%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=highlight%283%29 ALIGN=MIDDLE  ALT=\"y=highlight%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the y-intercept.<BR>\n" );
document.write( "The points called x-intercept and y-intercept are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A%28-5%2C0%29%29 ALIGN=MIDDLE  ALT=\"highlight%28A%28-5%2C0%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28B%280%2C3%29%29 ALIGN=MIDDLE  ALT=\"highlight%28B%280%2C3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > respectively.<BR>\n" );
document.write( " <BR>\n" );
document.write( "EXPLANATION:<BR>\n" );
document.write( "The x-intercept sometimes means the point where the line intersects the x-axis,<BR>\n" );
document.write( "but as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all points of the x-axis, that intersection point has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so its x-coordinate is also called the x-intercept of the line.<BR>\n" );
document.write( "Similarly, the point (with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) , or just its y-coordinate is called the y-intercept.<BR>\n" );
document.write( " <BR>\n" );
document.write( "b.<BR>\n" );
document.write( "Maybe you were taught that the slope of a line going through points <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%5BA%5D%2Cy%5BA%5D%29 ALIGN=MIDDLE  ALT=\"A%28x%5BA%5D%2Cy%5BA%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%28x%5BB%5D%2Cy%5BB%5D%29 ALIGN=MIDDLE  ALT=\"B%28x%5BB%5D%2Cy%5BB%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y%5BB%5D-y%5BA%5D%29%2F%28x%5BB%5D-x%5BA%5D%29 ALIGN=MIDDLE  ALT=\"m=%28y%5BB%5D-y%5BA%5D%29%2F%28x%5BB%5D-x%5BA%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Applied to the points found in part a,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%283-0%29%2F%280-%28-5%29%29=3%2F%280%2B5%29=3%2F5 ALIGN=MIDDLE  ALT=\"m=%283-0%29%2F%280-%28-5%29%29=3%2F%280%2B5%29=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28m=3%2F5%29 ALIGN=MIDDLE  ALT=\"highlight%28m=3%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "c.<BR>\n" );
document.write( "There is an infinite number of equivalent equations that represent the same line as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B5y=15 ALIGN=MIDDLE  ALT=\"-3x%2B5y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but there is only one that starts with \"y=\", and that is the slope-intercept form.<BR>\n" );
document.write( "To get it, we just solve for y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B5y=15 ALIGN=MIDDLE  ALT=\"-3x%2B5y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=3x%2B15 ALIGN=MIDDLE  ALT=\"5y=3x%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283x%2B15%29%2F5 ALIGN=MIDDLE  ALT=\"y=%283x%2B15%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2F5%2B15%2F5 ALIGN=MIDDLE  ALT=\"y=3x%2F5%2B15%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%283%2F5%29x%2B3%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%283%2F5%29x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "d.<BR>\n" );
document.write( "The slope-intercept form of the equation of a line is an equation of the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=m%2Ax%2Bb ALIGN=MIDDLE  ALT=\"y=m%2Ax%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the constants<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;\" ><BR>\n" );
document.write( "are the slope and y-intercept of the line respectively.<BR>\n" );
document.write( "The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2F5%29x%2B3 ALIGN=MIDDLE  ALT=\"y=%283%2F5%29x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > found in part c,<BR>\n" );
document.write( "tells us That <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;\" > is the slope (as found in part b),<BR>\n" );
document.write( "and that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the y-intercept (as found in part a). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );