document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195891>Question 1195891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 32 Portfolio Management A portfolio manager is concerned that two stocks generate an annual income of $15,000 for a client. The two stocks earn annual dividends of $2.40 and $3.50 per share, respectively. If x equals the number of shares of stock 1 and y equals the number of shares of stock 2, the equation\r<BR>\n" );
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document.write( "2.4x+3.5 15,000\r<BR>\n" );
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document.write( "states that total annual dividend income from the two stocks should total $15.000 Rewrite the equation in slope-intercept form and interpret the meaning of the slope and y intercept in this application. Solve for the x intercept and interpret its meaning. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828493 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=828493\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation is 2.4x + 3.5y = 15000<BR>\n" );
document.write( "x = number of shares of stock 1.<BR>\n" );
document.write( "y = number of shares of stock 2.<BR>\n" );
document.write( "this is a straight line equation in standard form.<BR>\n" );
document.write( "convert to slope intercept form by solving for y.<BR>\n" );
document.write( "subtract 2.4x from both sides of the equation to get 3.5y = 15000 - 2.4x<BR>\n" );
document.write( "divide both sides by 3.5 to get y = 15000/3.5 - 2.4x/3.5<BR>\n" );
document.write( "rearrange the equation in descending order of degree to get y = -2.4x/3.5 + 15000/3.5<BR>\n" );
document.write( "this is the same as y = -2.4/3.5 * x + 15000/3.5<BR>\n" );
document.write( "the equation is now in slope intercept form of y = mx + b<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept.<BR>\n" );
document.write( "m = -2.4/3.5<BR>\n" );
document.write( "b = 15000/3.5<BR>\n" );
document.write( "the y-intercept is the value of y when x = 0.<BR>\n" );
document.write( "y = -2.4/3.5  * 0 + 15000/3.5 which results in y = 15000/3.5 = 4285.714286 which is equal to 4285.714 rounded to 3 decimal places.<BR>\n" );
document.write( "the x-intercept is the value of x when y = 0 which results in 0 = -2.4/3.5 * x + 15000/3.5<BR>\n" );
document.write( "subtract 15000/3.5 from both sides of the equation to get -15000/3.5 = -2.4/3.5 * x<BR>\n" );
document.write( "solve for x to get x = (-15000/3.5) / (-2.4/3.5) = 6250.<BR>\n" );
document.write( "the equation can be graphed as shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/081601.jpg\"> </SPAN>\n" );
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