document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=224549>Question 224549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the slope intercept form of the equation of the line described.\r<BR>\n" );
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document.write( "through: (-3,-3), parallel to y=7/3x+3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167859 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=167859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the slope intercept form of the equation of the line described.\r<BR>\n" );
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document.write( "through: (-3,-3), parallel to y=7x/3+3\r<BR>\n" );
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document.write( "Step 1.  We can find the slope by recognizing that parallel lines have the same slope.  Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7x%2F3%2B3 ALIGN=MIDDLE  ALT=\"y=7x%2F3%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in slope-intercept form given as y=mx+b where the slope m=7/3 and the y-intercept b=3 when x=0 or at point (0,b) or (0,3).\r<BR>\n" );
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document.write( "Step 2.  Now we have to find the line with slope m=7/3 going through point (-3,-3).\r<BR>\n" );
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document.write( "Step 3.  Given two points (x1,y1) and (x2,y2), then the slope m is given as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"m=%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 4.  Let (x1,y1)=(-3,-3) or x1=-3 and y1=-3.  Let other point be ((x2,y2)=(x,y) or x2=x and y2=y.\r<BR>\n" );
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document.write( "Step 5.  Now we're given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=7%2F3 ALIGN=MIDDLE  ALT=\"m=7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Substituting above values and variables in the slope equation m yields the following steps:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"m=%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F3=%28y-%28-3%29%29%2F%28x-%28-3%29%29=%28y%2B3%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"7%2F3=%28y-%28-3%29%29%2F%28x-%28-3%29%29=%28y%2B3%29%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6.  Multiply x+3 to both sides to get rid of denominator on right side of equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28x%2B3%29%2F3=y%2B3 ALIGN=MIDDLE  ALT=\"7%28x%2B3%29%2F3=y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2F3%2B7%2A3%2F3=y%2B3 ALIGN=MIDDLE  ALT=\"7x%2F3%2B7%2A3%2F3=y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2F3%2B7=y%2B3 ALIGN=MIDDLE  ALT=\"7x%2F3%2B7=y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 7.  Now subtract 3 form both sides of equation to solve for y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2F3%2B7-3=y%2B3-3 ALIGN=MIDDLE  ALT=\"7x%2F3%2B7-3=y%2B3-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2F3%2B4=y ALIGN=MIDDLE  ALT=\"7x%2F3%2B4=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 8.  ANSWER:  The equation in slope-intercept form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7x%2F3%2B4 ALIGN=MIDDLE  ALT=\"y=7x%2F3%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note:  the above equation can be rewritten as \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x%2B3y=12 ALIGN=MIDDLE  ALT=\"-7x%2B3y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And the graph is shown below which is consistent with the above steps.\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7+x+%2B+3+y+=+12 ALIGN=MIDDLE  ALT=\"-7+x+%2B+3+y+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > describes a sloping line. For any <BR>\n" );
document.write( "  equation ax+by+c = 0, slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Fb+=+--7%2F3 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+--7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<UL><LI>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. 12/-7 = -1.71428571428571.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 12/3 = 4.</LI><LI>Slope is --7/3 = 2.33333333333333.</LI><LI> Equation in slope-intercept form: y=2.33333333333333*x+4.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-1.71428571428571-8%2C+-1.71428571428571%2B8%2C+4-8%2C+4%2B8%2C+2.33333333333333%2Ax%2B4+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
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document.write( "I hope the above steps and explanation were helpful.\r<BR>\n" );
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document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "And good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
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document.write( "http://www.FreedomUniversity.TV<BR>\n" );
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