document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196470>Question 1196470</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Variables x and y are such that when lg(2y+1) is plotted against x^2, a straight line graph passing through the points (1,1) and (2,5) is obtained. <BR>\n" );
document.write( "a) Find y in terms of x.<BR>\n" );
document.write( "b) find the value of y when x = √3/2.<BR>\n" );
document.write( "c) Find the value of x when y = 2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848493 by </B><A HREF=/tutors/aboutme.mpl?userid=proyaop><B>proyaop(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=proyaop><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=848493\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Determine the Equation of the Line**\r<BR>\n" );
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document.write( "* **Given Points:** (1, 1) and (2, 5) <BR>\n" );
document.write( "    * Where (x², lg(2y+1)) are the coordinates\r<BR>\n" );
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document.write( "* **Calculate Slope (m):**<BR>\n" );
document.write( "   * m = (y2 - y1) / (x2² - x1²) <BR>\n" );
document.write( "   * m = (5 - 1) / (2² - 1²) = 4 / 3\r<BR>\n" );
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document.write( "* **Calculate y-intercept (c):**<BR>\n" );
document.write( "   * Using point (1, 1): <BR>\n" );
document.write( "      * 1 = (4/3) * 1² + c <BR>\n" );
document.write( "      * c = 1 - 4/3 = -1/3\r<BR>\n" );
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document.write( "* **Equation of the line:**<BR>\n" );
document.write( "   * lg(2y+1) = (4/3)x² - 1/3\r<BR>\n" );
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document.write( "**2. Find y in terms of x (Part a)**\r<BR>\n" );
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document.write( "* lg(2y+1) = (4/3)x² - 1/3<BR>\n" );
document.write( "* 2y+1 = 10^[(4/3)x² - 1/3] <BR>\n" );
document.write( "* 2y = 10^[(4/3)x² - 1/3] - 1<BR>\n" );
document.write( "* y = [10^[(4/3)x² - 1/3] - 1] / 2\r<BR>\n" );
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document.write( "**3. Find the value of y when x = √3/2 (Part b)**\r<BR>\n" );
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document.write( "* y = [10^[(4/3)*(√3/2)² - 1/3] - 1] / 2<BR>\n" );
document.write( "* y = [10^[(4/3)*(3/4) - 1/3] - 1] / 2<BR>\n" );
document.write( "* y = [10^(1 - 1/3) - 1] / 2<BR>\n" );
document.write( "* y = [10^(2/3) - 1] / 2<BR>\n" );
document.write( "* y ≈ 1.8208\r<BR>\n" );
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document.write( "**4. Find the value of x when y = 2 (Part c)**\r<BR>\n" );
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document.write( "* lg(2*2 + 1) = (4/3)x² - 1/3<BR>\n" );
document.write( "* lg(5) = (4/3)x² - 1/3<BR>\n" );
document.write( "* (4/3)x² = lg(5) + 1/3<BR>\n" );
document.write( "* x² = 3/4 * (lg(5) + 1/3)<BR>\n" );
document.write( "* x = ± √[3/4 * (lg(5) + 1/3)]<BR>\n" );
document.write( "* x ≈ ± 0.8799\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* **a) y = [10^[(4/3)x² - 1/3] - 1] / 2**<BR>\n" );
document.write( "* **b) y ≈ 1.8208 when x = √3/2**<BR>\n" );
document.write( "* **c) x ≈ ± 0.8799 when y = 2**<BR>\n" );
document.write( " </SPAN>\n" );
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