document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=346098>Question 346098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find the intersecting points of two equations: y=.15x and y=.2(x-20)and graph them.  I have included my problem and what is expected.  I'm lost.\r<BR>\n" );
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document.write( "Ok this is what I got :<BR>\n" );
document.write( "You would set the two equations equal to each other and solve for x<BR>\n" );
document.write( "		.15x=.2(x-20) using the Elimination Method\r<BR>\n" );
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document.write( "Reorder the terms:<BR>\n" );
document.write( "0.15x = 0.2(-20 + x)<BR>\n" );
document.write( "0.15x = (-20 * 0.2 + x * 0.2)<BR>\n" );
document.write( "0.15x = (-4 + 0.2x)\r<BR>\n" );
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document.write( "Solving<BR>\n" );
document.write( "0.15x = -4 + 0.2x\r<BR>\n" );
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document.write( "Solving for variable 'x'.\r<BR>\n" );
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document.write( "Move all terms containing x to the left, all other terms to the right.\r<BR>\n" );
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document.write( "Add '-0.2x' to each side of the equation.<BR>\n" );
document.write( "0.15x + -0.2x = -4 + 0.2x + -0.2x\r<BR>\n" );
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document.write( "Combine like terms: 0.15x + -0.2x = -0.05x<BR>\n" );
document.write( "-0.05x = -4 + 0.2x + -0.2x\r<BR>\n" );
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document.write( "Combine like terms: 0.2x + -0.2x = 0.0<BR>\n" );
document.write( "-0.05x = -4 + 0.0<BR>\n" );
document.write( "-0.05x = -4\r<BR>\n" );
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document.write( "Divide each side by '-0.05'.<BR>\n" );
document.write( "x = 80\r<BR>\n" );
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document.write( "Simplifying<BR>\n" );
document.write( "x = 80\r<BR>\n" );
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document.write( "Now that X = 80, I plugged it into the equation y=0.15x and got this:<BR>\n" );
document.write( "y=0.15x   <BR>\n" );
document.write( "y=0.15(80) <BR>\n" );
document.write( "y= 12\r<BR>\n" );
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document.write( "Now this is the question to my problem and I do not know how to get the answer. I have to graph this and show the intersection.\r<BR>\n" );
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document.write( "a teacher is looking for the best option in purchasing school supplies for a classroom.  Where Company A is offering a discount for every dollar amount spent on school supplies and where Company B is offering a higher discount than Company A, but the discount for Company B is only offered for every dollar amount spent above $20.00.  I will determine and explain which company will offer a better price based upon the dollar amount the teacher spends on school supplies.\r<BR>\n" );
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document.write( "Option 1- Company A will offer her a 15% discount on the total amount spent in the store. <BR>\n" );
document.write( "Option 2- Company B will offer her a 20% discount on the remaining amount after the first $20 is spent.\r<BR>\n" );
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document.write( "Depict the situation graphically, using appropriate graphing software such as Excel or an online graphing utility.\r<BR>\n" );
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document.write( "Include the following in your graph:<BR>\n" );
document.write( "•  A depiction of each cost option on the same graph<BR>\n" );
document.write( "• Clear labels of the cost to the hypothetical customer for both options on the graph <BR>\n" );
document.write( "• The intersection of the cost options (if one exists)\r<BR>\n" );
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document.write( "I'm so lost.  I do not know how to graph this. Please help if you can.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #247480 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=247480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First your answer is correct. <BR>\n" );
document.write( "Now plotting.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.15x ALIGN=MIDDLE  ALT=\"y=0.15x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=100 ALIGN=MIDDLE  ALT=\"x=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=15 ALIGN=MIDDLE  ALT=\"y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Plot the points and the line connecting them.<BR>\n" );
document.write( "The x-axis is the amount of money you spend.<BR>\n" );
document.write( "The y-axis is the discount you receive.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C+-10%2C140%2C-2%2C18+%2C+grid%281%29%2C+circle%280%2C0%2C2.3%29%2Ccircle%28100%2C15%2C2.3%29%2Cgraph%28300%2C300%2C+-10%2C140%2C-2%2C18+%2C0.15x%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The red line is the savings from the Company A plan.<BR>\n" );
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document.write( "The Company B savings only begins at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=20 ALIGN=MIDDLE  ALT=\"x=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "So you have to spend at least $20 to receive any discount.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=.2%28x-20%29 ALIGN=MIDDLE  ALT=\"y=.2%28x-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=20 ALIGN=MIDDLE  ALT=\"x=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=0 ALIGN=MIDDLE  ALT=\"+y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=100 ALIGN=MIDDLE  ALT=\"x=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.2%28100-20%29=16 ALIGN=MIDDLE  ALT=\"y=0.2%28100-20%29=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plot those points and line.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C140%2C-2%2C18%2Cgrid%281%29%2Ccircle%2820%2C0%2C2.3%29%2Ccircle%28100%2C16%2C2.3%29%2Cblue%28line%2820%2C0%2C220%2C40%29%29%2Ccircle%280%2C0%2C2.3%29%2Ccircle%28100%2C15%2C2.3%29%2Cgraph%28300%2C300%2C-10%2C140%2C-2%2C18%2C0.15x%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The blue line is the savings from the Company B plan.<BR>\n" );
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document.write( "When does the Company B plan savings equal the Company A plan savings.<BR>\n" );
document.write( "You already calculated that point. <BR>\n" );
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document.write( "When you spend $80, you get a savings from both plans of $12.<BR>\n" );
document.write( "Plot that point too.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C+-10%2C140%2C-2%2C18+%2Cgrid%281%29%2Ccircle%2820%2C0%2C2.3%29%2Ccircle%28100%2C16%2C2.3%29%2Cblue%28line%2820%2C0%2C220%2C40%29%29%2Ccircle%280%2C0%2C2.3%29%2Ccircle%2880%2C12%2C2%29%2Ccircle%28100%2C15%2C2.3%29%2Cgraph%28300%2C300%2C-10%2C140%2C-2%2C18%2C0.15x%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Once you pass that point ($80), Company B savings (blue line) are higher than Company A.<BR>\n" );
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document.write( "If you spend less than $80, Company A savings (red line) are higher than Company B.<BR>\n" );
document.write( " </SPAN>\n" );
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