document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172310>Question 1172310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a design of a highway, a survey for the hill side shows that it is in the following <BR>\n" );
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document.write( "a)	Y= 2X-3 ; Y  given the value of  X BETWEEN  -3.5 TO + 5.5 . State the typical standard straight line formula; Draw Straight Line GRAPH for the two formula and Find the steps in the ratio the  Y value of the Gradient.                                     \r<BR>\n" );
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document.write( "b)	2Y= 8X-1 ; given the value of  X BETWEEN  -3.2 TO + 6.3 . State the typical standard straight line formula; Draw Straight Line GRAPH for the formula and Find the steps in the ratio the Y value of the Gradient.                                                                      \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850824 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850824\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Absolutely! Let's break down each part of the problem.\r<BR>\n" );
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document.write( "**a) Y = 2X - 3**\r<BR>\n" );
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document.write( "1.  **Standard Straight Line Formula:**<BR>\n" );
document.write( "    * The typical standard straight-line formula is y = mx + b, where:<BR>\n" );
document.write( "        * m is the slope (gradient) of the line.<BR>\n" );
document.write( "        * b is the y-intercept (the value of y when x = 0).<BR>\n" );
document.write( "    * In this case, y = 2x - 3, so:<BR>\n" );
document.write( "        * m = 2<BR>\n" );
document.write( "        * b = -3\r<BR>\n" );
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document.write( "2.  **Straight Line Graph:**<BR>\n" );
document.write( "    * To draw the graph, you can:<BR>\n" );
document.write( "        * Choose a few values of x within the given range (-3.5 to 5.5).<BR>\n" );
document.write( "        * Calculate the corresponding y values.<BR>\n" );
document.write( "        * Plot the points (x, y) on a coordinate plane.<BR>\n" );
document.write( "        * Draw a straight line through the points.<BR>\n" );
document.write( "    * Here's how to calculate a couple of points.<BR>\n" );
document.write( "        * if x = 0, y = 2(0) - 3 = -3. (0, -3)<BR>\n" );
document.write( "        * if x = 1, y = 2(1) - 3 = -1. (1, -1)\r<BR>\n" );
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document.write( "3.  **Steps in the Ratio of the Y Value of the Gradient:**<BR>\n" );
document.write( "    * The gradient (slope) is 2. This means that for every 1 unit increase in x, y increases by 2 units.<BR>\n" );
document.write( "    * The ratio of the change in y to the change in x is 2/1.\r<BR>\n" );
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document.write( "**b) 2Y = 8X - 1**\r<BR>\n" );
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document.write( "1.  **Standard Straight Line Formula:**<BR>\n" );
document.write( "    * First, we need to rearrange the equation to the standard form (y = mx + b):<BR>\n" );
document.write( "        * 2y = 8x - 1<BR>\n" );
document.write( "        * y = 4x - 1/2<BR>\n" );
document.write( "    * Now, we can identify:<BR>\n" );
document.write( "        * m = 4<BR>\n" );
document.write( "        * b = -1/2\r<BR>\n" );
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document.write( "2.  **Straight Line Graph:**<BR>\n" );
document.write( "    * Similar to part a, choose x values within the range (-3.2 to 6.3), calculate y values, and plot the points.<BR>\n" );
document.write( "    * Here are a few points.<BR>\n" );
document.write( "        * if x = 0, y = 4(0) - 1/2 = -1/2 (0, -0.5)<BR>\n" );
document.write( "        * if x = 1, y = 4(1) - 1/2 = 3.5 (1, 3.5)\r<BR>\n" );
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document.write( "3.  **Steps in the Ratio of the Y Value of the Gradient:**<BR>\n" );
document.write( "    * The gradient (slope) is 4. This means that for every 1 unit increase in x, y increases by 4 units.<BR>\n" );
document.write( "    * The ratio of the change in y to the change in x is 4/1.\r<BR>\n" );
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document.write( "**Gradient Comparison**\r<BR>\n" );
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document.write( "* The gradient of the first line (y = 2x - 3) is 2.<BR>\n" );
document.write( "* The gradient of the second line (y = 4x - 1/2) is 4.<BR>\n" );
document.write( "* The second line has a steeper slope than the first line.<BR>\n" );
document.write( "* The second line's gradient is twice that of the first line. (4/2 = 2)<BR>\n" );
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