document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84645>Question 84645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could I possibly get some help on these problems?\r<BR>\n" );
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document.write( "Write the equation of the line passing through <BR>\n" );
document.write( "(4,4) and (4,2).\r<BR>\n" );
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document.write( "Write the equation of the line which has y-intercept (0,5) and is perpendicular to the line with equation y=-3x+1.\r<BR>\n" );
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document.write( "A roof rises 9.75 ft. over a horizontal distance of 17.24 ft.  What is the slope of the roof to the nearest hundreth?\r<BR>\n" );
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document.write( "Given f(x)=5x2-3x+1, find f(-2).\r<BR>\n" );
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document.write( "thank you for your time and help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61013 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=61013\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ******************<BR>\n" );
document.write( "Write the equation of the line passing through (4,4) and (4,2).<BR>\n" );
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document.write( "The \"trick\" to this problem is to note that the value of x in both of the given points is<BR>\n" );
document.write( "the same.  So you can say that based on these two points, the value of y can be anything<BR>\n" );
document.write( "but the value of x always equals 4.  So the equation that reflects this situation <BR>\n" );
document.write( "is x = 4. That is the answer to this question.  (The graph of this equation is a vertical<BR>\n" );
document.write( "line that crosses the x-axis at +4.)<BR>\n" );
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document.write( "Write the equation of the line which has y-intercept (0,5) and is perpendicular to the line with equation y=-3x+1.<BR>\n" );
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document.write( "For two lines to be perpendicular their slopes must be negative inverses of each other.<BR>\n" );
document.write( "For example, if one of the lines has a slope of 4, to be perpendicular to it the other<BR>\n" );
document.write( "line must have a slope of -1/4.  In this case, the given line has a slope of -3. (You can<BR>\n" );
document.write( "tell that because -3 is the multiplier of the x term in the equation of the line.) Therefore,<BR>\n" );
document.write( "the slope of a line that is perpendicular to the given line must be -1/(-3).  This simplifies<BR>\n" );
document.write( "to +1/3.  The slope intercept form of an equation can be used.  This form is:<BR>\n" );
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document.write( "y = mx + b <BR>\n" );
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document.write( "where m is the slope and b is the value where the graph crosses the y-axis.  We have<BR>\n" );
document.write( "figured out that the slope of the perpendicular line is +1/3 so we can substitute <BR>\n" );
document.write( "that into the slope intercept form.  When we do that the equation becomes:<BR>\n" );
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document.write( "y = (1/3)x + b<BR>\n" );
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document.write( "The problem also tells you that the y-intercept point of the perpendicular line is (0,5).<BR>\n" );
document.write( "This means that the value of y where the graph of the perpendicular crosses the y-axis <BR>\n" );
document.write( "is +5.  But that point is represented by b in the equation. Therefore, substitute<BR>\n" );
document.write( "+5 for b and the equation of the perpendicular line becomes:<BR>\n" );
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document.write( "y = (1/3)x + 5<BR>\n" );
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document.write( "and this is the equation you were asked to find.<BR>\n" );
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document.write( "A roof rises 9.75 ft. over a horizontal distance of 17.24 ft.  What is the slope of the roof to the nearest hundreth?<BR>\n" );
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document.write( "Slope is defined as rise divided by horizontal distance which is called run.  In this <BR>\n" );
document.write( "problem you are told that the rise is 9.75 feet and the run is 17.24 feet. So the slope (m)<BR>\n" );
document.write( "is:<BR>\n" );
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document.write( "m = 9.75/17.24<BR>\n" );
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document.write( "Using a calculator you can reduce this:<BR>\n" );
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document.write( "m = 9.75/17.24 = 0.565545243<BR>\n" );
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document.write( "and to the nearest hundredth this rounds to 0.57<BR>\n" );
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document.write( "The answer to this problem is that the slope is 0.57<BR>\n" );
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document.write( "Given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=5x%5E2-3x%2B1 ALIGN=MIDDLE  ALT=\"f%28x%29=5x%5E2-3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >    find f(-2).<BR>\n" );
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document.write( "All that this problem is asking you to do is to evaluate f(x) when x = -2.  So all you<BR>\n" );
document.write( "need to do is substitute -2 for x and calculate out the answer.<BR>\n" );
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document.write( "When x is -2, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2-3x%2B1 ALIGN=MIDDLE  ALT=\"5x%5E2-3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28-2%29%5E2+-+%283%2A%28-2%29%29+%2B+1 ALIGN=MIDDLE  ALT=\"5%2A%28-2%29%5E2+-+%283%2A%28-2%29%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%5E2+=+4 ALIGN=MIDDLE  ALT=\"%28-2%29%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%28-2%29+=+-6 ALIGN=MIDDLE  ALT=\"3%2A%28-2%29+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > the problem becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%29-+%28-6%29+%2B+1 ALIGN=MIDDLE  ALT=\"%285%2A4%29-+%28-6%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+%2B+6+%2B+1+=+27 ALIGN=MIDDLE  ALT=\"20+%2B+6+%2B+1+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The answer is f(-2) = 27\r<BR>\n" );
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document.write( "Hope this helps you to understand these four problems a little better. </SPAN>\n" );
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