document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=226304>Question 226304</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the equation for a line that contains the points (0,4) and is parallel to y=2x+3? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #168558 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=168558\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the equation for a line that contains the points (0,4) and is parallel to y=2x+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=2x%2B3 ALIGN=MIDDLE  ALT=\"y=2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in slope-intercept form given as y=mx+b where the slope m=2 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=2 going through point (0,4).\r<BR>\n" );
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document.write( "But the point (0,4) is the y-intercept.  Then y=2x+4.  \r<BR>\n" );
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document.write( "The next sequence of steps will show the same equation but this method is applicable even when the point is not the y-intercept.\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)=(0,4) or x1=2 and y1=0.  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=2 ALIGN=MIDDLE  ALT=\"m=2\"   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=2=%28y-4%29%2F%28x-0%29=%28y-4%29%2Fx ALIGN=MIDDLE  ALT=\"2=%28y-4%29%2F%28x-0%29=%28y-4%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6.  Multiply x 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=2x=x%2A%28y-4%29%2Fx ALIGN=MIDDLE  ALT=\"2x=x%2A%28y-4%29%2Fx\"   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=2x=y-4 ALIGN=MIDDLE  ALT=\"2x=y-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and after adding 4 to both sides yields <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B4 ALIGN=MIDDLE  ALT=\"y=2x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > same result as before.\r<BR>\n" );
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document.write( "Step 7.  ANSWER:  The equation in slope-intercept form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B4 ALIGN=MIDDLE  ALT=\"y=2x%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=-2x%2By=4 ALIGN=MIDDLE  ALT=\"-2x%2By=4\"   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=-2+x+%2B+1+y+=+4 ALIGN=MIDDLE  ALT=\"-2+x+%2B+1+y+=+4\"   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+=+--2%2F1 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+--2%2F1\"   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. 4/-2 = -2.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 4/1 = 4.</LI><LI>Slope is --2/1 = 2.</LI><LI> Equation in slope-intercept form: y=2*x+4.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-2-8%2C+-2%2B8%2C+4-8%2C+4%2B8%2C+2%2Ax%2B4+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-2-8%2C+-2%2B8%2C+4-8%2C+4%2B8%2C+2%2Ax%2B4+%29+\"   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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