document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90579>Question 90579</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0536753601/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this equation.<BR>\n" );
document.write( "Graph the following,<BR>\n" );
document.write( "The line that has a slope of -2 and passes through the point(-3,5)<BR>\n" );
document.write( "Thank You, </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65756 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=65756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since you are given the slope of the graph, it makes sense to use the slope-intercept<BR>\n" );
document.write( "form of an equation.  This form is:<BR>\n" );
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document.write( "y = mx + b<BR>\n" );
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document.write( "in which m is the slope.  The problem tells you that the slope is -2, so in the slope-intercept<BR>\n" );
document.write( "form you can substitute -2 for m and the equation then becomes:<BR>\n" );
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document.write( "y = -2x + b<BR>\n" );
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document.write( "The problem also tells you that the point (-3, 5) is on the graph.  This means that the<BR>\n" );
document.write( "equation is satisfied when x equals -3 and y equals +5. So in the slope-intercept equation<BR>\n" );
document.write( "that we are working on you can substitute -3 for x and +5 for y to get:<BR>\n" );
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document.write( "+5 = (-2)(-3) + b<BR>\n" );
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document.write( "Do the multiplication on the right side to get:<BR>\n" );
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document.write( "+5 = +6 + b<BR>\n" );
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document.write( "Solve for b by subtracting +6 from both sides and you have:<BR>\n" );
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document.write( "-1 = b<BR>\n" );
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document.write( "So now you know that the slope m is -2 and the value of b (which is the point on the y-axis<BR>\n" );
document.write( "where the graph crosses that axis) is -1. Substitute those two values into the slope-intercept<BR>\n" );
document.write( "form and the equation becomes:<BR>\n" );
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document.write( "y = -2x - 1<BR>\n" );
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document.write( "That is the equation you are trying to graph. Since you now know that the graph crosses the<BR>\n" );
document.write( "y-axis at the point y = -1, you can put a dot on the graph at that point. Then you know<BR>\n" );
document.write( "that the graph slopes at the rate -2 meaning that for every 1 unit you go horizontally<BR>\n" );
document.write( "you move 2 units down. Put your pencil at the point -1 on the y-axis. Then move horizontally<BR>\n" );
document.write( "1 unit ... stop there and then move down vertically 2 units and put a dot there. You should<BR>\n" );
document.write( "be at the point (1, -3) and that point is on the graph.  From that point you can again move<BR>\n" );
document.write( "horizontally 1 unit and then down vertically 2 units. You should be at the point (2, -5) and<BR>\n" );
document.write( "that point is on the graph.  You can also plot the given point (-3, 5) as a point on the graph. <BR>\n" );
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document.write( "This gives you 4 points on the graph ... (-3, 5), (0, -1), (1, -3) and (2, -5). These points<BR>\n" );
document.write( "can then be connected by running a straight line through them and that is the graph.<BR>\n" );
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document.write( "Another way you could locate points is to go to the equation we developed:<BR>\n" );
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document.write( "y = -2x - 1<BR>\n" );
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document.write( "and assign values that you choose for x and calculate the corresponding value of y. For example,<BR>\n" );
document.write( "suppose you choose to let x = -1. Substitute that value into the equation and you get:<BR>\n" );
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document.write( "y = (-2)(-1) - 1 = +2 - 1 = +1<BR>\n" );
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document.write( "This tells you that when x = -1 then y = +1, so the point (-1, +1) is on the graph.<BR>\n" );
document.write( "You can repeat this process for other values of x to get other points that can be connected<BR>\n" );
document.write( "to give you the graph. When you get enough points to satisfy yourself that you know what<BR>\n" );
document.write( "the graph looks like, you can run a straight line through the points to see the graph.<BR>\n" );
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document.write( "The graph should look like:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C5%2C-10%2C7%2C-2%2Ax+-1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C5%2C-10%2C7%2C-2%2Ax+-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the process that you can use to solve this problem. </SPAN>\n" );
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