document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118341>Question 118341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> White each equation in slope-intercept form.<BR>\n" );
document.write( "#9 3.4\r<BR>\n" );
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document.write( "3x - 4y = 80\r<BR>\n" );
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document.write( "#21 3.4<BR>\n" );
document.write( "find the equation of the line that goes through the given point and has the given slope.  Write the answer in slope-intercept form.\r<BR>\n" );
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document.write( "(-1, -7), -6 \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 #86455 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=86455\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For reference: <BR>\n" );
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document.write( "The slope-intercept form of an equation is y = mx + b<BR>\n" );
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document.write( "In this form, m (the multiplier of x) is the slope of the line and b (a constant) is the<BR>\n" );
document.write( "value on the y-axis where the line intercepts the y-axis.<BR>\n" );
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document.write( "Given for the first problem:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+-+4y+=+80 ALIGN=MIDDLE  ALT=\"3x+-+4y+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice in the slope intercept form you want y to be by itself on the left side of the equal<BR>\n" );
document.write( "sign. So for this problem we begin by getting rid of the 3x term on the left side by subtracting<BR>\n" );
document.write( "3x from both sides of the equation. After subtracting 3x from both sides you are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y+=+-3x+%2B+80 ALIGN=MIDDLE  ALT=\"-4y+=+-3x+%2B+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To just have y on the left side, you now divide both sides (all terms) by -4 and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28%28-3%29%2F-4%29%2Ax+%2B+80 ALIGN=MIDDLE  ALT=\"y+=+%28%28-3%29%2F-4%29%2Ax+%2B+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In the fraction that multiplies x you have a minus sign in both the numerator and the <BR>\n" );
document.write( "denominator. Since this means you are dividing two minus quantities, the answer will be <BR>\n" );
document.write( "positive and you end up with the answer to this problem ... the slope-intercept form of:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2F4%29%2Ax+%2B+80 ALIGN=MIDDLE  ALT=\"y+=+%283%2F4%29%2Ax+%2B+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "in which the slope (or multiplier of x) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the place where the graphed line<BR>\n" );
document.write( "for this equation crosses the y-axis is at +80 on the y-axis.<BR>\n" );
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document.write( "Again, the answer to the first problem is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2F4%29%2Ax+%2B+80 ALIGN=MIDDLE  ALT=\"y+=+%283%2F4%29%2Ax+%2B+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "For the second problem you to find the slope-intercept equation of a line that goes through<BR>\n" );
document.write( "the point (-1, -7) and has a slope equal to -6.<BR>\n" );
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document.write( "Again, the slope intercept form equation is y = mx + b where m is the slope. Since the<BR>\n" );
document.write( "problem tells you that the slope is -6 you can substitute that value for m to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-6%2Ax+%2B+b ALIGN=MIDDLE  ALT=\"y+=+-6%2Ax+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next, you need to solve for b. You are told by the problem that when x equals -1 and y equals -7<BR>\n" );
document.write( "the equation for the line will be satisfied. That is because the (x, y) point (-1, -7) is on<BR>\n" );
document.write( "the line. So substitute -1 for x and -7 for y to get that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-6%2Ax+%2B+b ALIGN=MIDDLE  ALT=\"y+=+-6%2Ax+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7+=+-6%2A%28-1%29+%2B+b ALIGN=MIDDLE  ALT=\"-7+=+-6%2A%28-1%29+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Do the multiplication on the right side ... -6 times -1 and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7+=+%2B6+%2B+b ALIGN=MIDDLE  ALT=\"-7+=+%2B6+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the +6 on the right side by subtracting 6 from both sides and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-13+=+b ALIGN=MIDDLE  ALT=\"-13+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now that you know that b = -13 you can return to the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-6%2Ax+%2B+b ALIGN=MIDDLE  ALT=\"y+=+-6%2Ax+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and substitute -13 for b to get that the slope-intercept form of the equation that has a <BR>\n" );
document.write( "slope of - 6 and goes through the point (-1, -7) is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-6%2Ax+-+13 ALIGN=MIDDLE  ALT=\"y+=+-6%2Ax+-+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this is the answer to the second problem. You can check it by substituting -1 for x<BR>\n" );
document.write( "and find out if the corresponding value of y is -7 ... just as you were told it should be<BR>\n" );
document.write( "in the problem. (It is, so the problem checks.)<BR>\n" );
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document.write( "Hope this helps you to understand the two problems and how you can solve them both.<BR>\n" );
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