document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116283>Question 116283</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me with these questions? I did not get this out of a book, it was a handout. The question is: Find the x  and  y intercepts and then graph <BR>\n" );
document.write( " x-y=2 , -x+4y=4  and y = -4x -4. I do not fully understand the question.<BR>\n" );
document.write( "Any help on this is greatly appreciated. Can you explain it step by step, not leaving anything out , please.\r<BR>\n" );
document.write( "\n" );
document.write( "Thankyou<BR>\n" );
document.write( "Laurie </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84587 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84587\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> :<BR>\n" );
document.write( "I will try to be very detailed on the 1st one, hopefully by the time you get to the 2nd one you will have an idea what's going on.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the x and y intercepts and then graph<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x - y = 2<BR>\n" );
document.write( "First we want to put the equation in the \"y =\"; subtract x from both sides:<BR>\n" );
document.write( "-y = -x - 2<BR>\n" );
document.write( "y has to be positive in this form, multiply equation by -1 and you have:<BR>\n" );
document.write( "y = x + 2 <BR>\n" );
document.write( ":<BR>\n" );
document.write( "The x intercept occurs when y = 0, therefore make y = 0 and solve for x:<BR>\n" );
document.write( "x + 2 = y<BR>\n" );
document.write( "x + 2 = 0<BR>\n" );
document.write( "x = -2; this is the x intercept<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The y intercept occurs when x = 0; substitute 0 for x in our equation, find y:<BR>\n" );
document.write( "y = x + 2<BR>\n" );
document.write( "y = 0 + 2<BR>\n" );
document.write( "y = +2; this is the y intercept<BR>\n" );
document.write( ":<BR>\n" );
document.write( "To graph this we need at least two x,y points, choose convenient values for x:<BR>\n" );
document.write( " let x = -3 and let x = +3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Substitute -3 for x:<BR>\n" );
document.write( "y = x + 2<BR>\n" );
document.write( "y = -3 + 2<BR>\n" );
document.write( "y = -1<BR>\n" );
document.write( "Plot x=-3, y=-1 on a standard  +/-10 graph<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2nd point: x = +3<BR>\n" );
document.write( "y = x + 2<BR>\n" );
document.write( "y = 3 + 2<BR>\n" );
document.write( "y = +5<BR>\n" );
document.write( "Plot x=3, y=5 on the same graph, join points with a straight line, this is the graph<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Should look like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x%2B2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that it confirms are values for the x and y intercepts<BR>\n" );
document.write( "The graph crosses the vertical line where y=2, (the y intercept)<BR>\n" );
document.write( "The graph crossed the horizontal line where x = -2; (the x intercept)<BR>\n" );
document.write( ":<BR>\n" );
document.write( ": <BR>\n" );
document.write( "-x + 4y = 4<BR>\n" );
document.write( "Put equation into the y= form, add x to both sides<BR>\n" );
document.write( "4y = x + 4<BR>\n" );
document.write( "y has to have a coefficient of 1, divide both sides by 4 and you have:<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F4 ALIGN=MIDDLE  ALT=\"4%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = .25x + 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The x intercept (y=0):<BR>\n" );
document.write( ".25x + 1 = y<BR>\n" );
document.write( ".25x + 1 = 0<BR>\n" );
document.write( ".25x = -1<BR>\n" );
document.write( "x has to have a coefficient of 1, multiply both sides by 4 and you have;<BR>\n" );
document.write( "x = -4; is the x intercept<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The y intercept (x=0)<BR>\n" );
document.write( "y = .25x + 1<BR>\n" );
document.write( "y = .25(0) = 1<BR>\n" );
document.write( "y = 0 + 1<BR>\n" );
document.write( "y = 1 is the y intercept<BR>\n" );
document.write( ":<BR>\n" );
document.write( "two x,y points, choose some convenient values for x:<BR>\n" );
document.write( "  let x = -3 and let x = +3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Substitute -3 for x:<BR>\n" );
document.write( "y = .25x + 1<BR>\n" );
document.write( "y = .25(-3) + 1<BR>\n" );
document.write( "y = -.75 + 1<BR>\n" );
document.write( "y = +.25<BR>\n" );
document.write( "Plot x=-3, y=+.25 <BR>\n" );
document.write( ":<BR>\n" );
document.write( "2nd point: x = +3<BR>\n" );
document.write( "y = .25(3) + 1<BR>\n" );
document.write( "y = .75 + 1<BR>\n" );
document.write( "y = +1.75<BR>\n" );
document.write( "Plot x=3, y=1.75 on the same graph, join points with a straight line, this is the graph.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Should look like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+.25x%2B1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+.25x%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that it confirms are values for the x and y intercepts<BR>\n" );
document.write( "The graph crosses the vertical line where y=1, (the y intercept)<BR>\n" );
document.write( "The graph crossed the horizontal line where x = -4; (the x intercept)<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "y = -4x - 4 this one is already in the form we want it:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x intercept (y=0)<BR>\n" );
document.write( "-4x -4 = y<BR>\n" );
document.write( "-4x - 4 = 0<BR>\n" );
document.write( "-4x = +4; added 4 to both sides:<BR>\n" );
document.write( "x = -1; divided both sides by -4 to make the coefficient of x a +1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "y intercept (x=0)<BR>\n" );
document.write( "y = -4(0) - 4<BR>\n" );
document.write( "y = -4; <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Graph this equation the same way, it is more convenient to use x = -2 and x = +1<BR>\n" );
document.write( "This is to keep the points on a +/-10 xy graph.<BR>\n" );
document.write( "Substitute -2 for x:<BR>\n" );
document.write( "y = -4x - 4 <BR>\n" );
document.write( "y = -4(-2) - 4<BR>\n" );
document.write( "y =  +8 - 4<BR>\n" );
document.write( "y = +4<BR>\n" );
document.write( "Plot x=-2, y=+4 <BR>\n" );
document.write( ":<BR>\n" );
document.write( "2nd point: x = +1<BR>\n" );
document.write( "y = -4(1) - 4<BR>\n" );
document.write( "y = -4 - 4<BR>\n" );
document.write( "y = -8<BR>\n" );
document.write( "Plot x=1, y=-8 on the same graph, join points with a straight line, <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Should look like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+-4x-4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+-4x-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that it confirms are values for the x and y intercepts<BR>\n" );
document.write( "The graph crosses the vertical line where y=-4, (the y intercept)<BR>\n" );
document.write( "The graph crossed the horizontal line where x = -1; (the x intercept)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "It tried to make things clear here, if you have any questions about this concept you can email me. A<BR>\n" );
document.write( ":\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );