document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113203>Question 113203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help on the following questions:I am having a hard time with finding slopes and writing the following equations. I would really appreciate your help,thank you in advance.<BR>\n" );
document.write( "1.Find the slope of the line passing through the points (-3,1) and (-6,10)<BR>\n" );
document.write( "2. Write the equation of the line with slope -5 and y intercept (0,5)<BR>\n" );
document.write( "3. Write the equation of the line with x-intercept (-1,0) and undefined slope </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82388 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82388\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the slope of a line given two points, the first thing to decide is which will be Point 1 and which Point 2.  It doesn't matter which you pick, as long as you keep it consistent as you solve the problem.\r<BR>\n" );
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document.write( "Let's say that your point (-3, 1) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B1%5D ALIGN=MIDDLE  ALT=\"P%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and (-6, 10) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B2%5D ALIGN=MIDDLE  ALT=\"P%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The coordinates of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B1%5D ALIGN=MIDDLE  ALT=\"P%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=-3 ALIGN=MIDDLE  ALT=\"x%5B1%5D=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=1 ALIGN=MIDDLE  ALT=\"y%5B1%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and \r<BR>\n" );
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document.write( "The coordinates of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B2%5D ALIGN=MIDDLE  ALT=\"P%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=-6 ALIGN=MIDDLE  ALT=\"x%5B2%5D=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D=10 ALIGN=MIDDLE  ALT=\"y%5B2%5D=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we can use the formula for the slope to compute it.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29=%281-10%29%2F%28-3-%28-6%29%29=%28-9%29%2F3=-3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The slope-intercept form of a straight line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > where m is the slope and b is the y-coordinate of the y-intercept.  The y-intercept is the point where the line intersects the y-axis, in other words, the value of y when x = 0.\r<BR>\n" );
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document.write( "Given that the slope of the line is -5 and the y-intercept is (0, 5), we can write the equation directly by substitution in the slope-intercept form.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5x%2B5 ALIGN=MIDDLE  ALT=\"y=-5x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Can you see that if you put 0 in for x in this equation that y = 5?\r<BR>\n" );
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document.write( "A line with an undefined slope is a line where all of the x-coordinate points are equal.  That means that if you tried to compute the slope, the slope formula, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29 ALIGN=MIDDLE  ALT=\"m=%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > would have a zero denominator.  Such a line must be a vertical line for all of the x-coordinates to be equal. \r<BR>\n" );
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document.write( "Since all of the x-coordinates are equal, we know what that value is from the x-coordinate of the x-intercept, (-1, 0).  Since x = -1 for all values of y, the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > fully describes the line and is therefore the sought after equation.\r<BR>\n" );
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document.write( "Hope this helps,<BR>\n" );
document.write( "John </SPAN>\n" );
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