document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=430081>Question 430081</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which point lies on the line represented by the equation below?<BR>\n" );
document.write( "5x + 4y = 22 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #298662 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=298662\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a whole bunch of points lie on the line represented by the equation.\r<BR>\n" );
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document.write( "to find them, you need to solve for either y or x.\r<BR>\n" );
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document.write( "most time you solve for y.\r<BR>\n" );
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document.write( "this makes y the dependent variable and x the independent variable.\r<BR>\n" );
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document.write( "being independent, you can choose any value you want for x and then use the equation to solve for y.\r<BR>\n" );
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document.write( "you could eave the equation as is and then solve for y, or you can solve for y and then plug in the values for x.\r<BR>\n" );
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document.write( "we'll solve for y first and then plug values in for x to find values of y that satisfy the equation.\r<BR>\n" );
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document.write( "if the values of y satisfy the equation, then the coordinate (x,y) pair created by combining that x with that y will be on the line.\r<BR>\n" );
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document.write( "your equation is:\r<BR>\n" );
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document.write( "5x + 4y = 22\r<BR>\n" );
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document.write( "we solve for y as follows:\r<BR>\n" );
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document.write( "subtract 5x from both sides of the equation to get:\r<BR>\n" );
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document.write( "4y = -5x + 22\r<BR>\n" );
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document.write( "divide both sides of the equation by 4 to get:\r<BR>\n" );
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document.write( "y = (-5/4)x + (22/4)\r<BR>\n" );
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document.write( "you have just solved for y.\r<BR>\n" );
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document.write( "now you can take any value of x and plug it into the equation to solve for y.\r<BR>\n" );
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document.write( "we'll take x = 0.\r<BR>\n" );
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document.write( "when x = 0, the equation becomes:\r<BR>\n" );
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document.write( "y = (-5/4)*0 + (22/4) which becomes y = (22/4).\r<BR>\n" );
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document.write( "the coordinate pair of (x,y) we now have is (0,(22/4).\r<BR>\n" );
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document.write( "that point is on the line because the value of y we calculated satisfies the equation when x = 0.\r<BR>\n" );
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document.write( "that value of y, by the way, is the y-intercept of the equation.   the y-intercept of the equation is the value of y when x = 0.\r<BR>\n" );
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document.write( "if we want to find the x-intercept of the equation, then we set the value of y equal to 0 and solve for x.\r<BR>\n" );
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document.write( "our equation is:\r<BR>\n" );
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document.write( "y = (-5/4)x + (22/4)\r<BR>\n" );
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document.write( "when we set y equal to 0, the equation becomes:\r<BR>\n" );
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document.write( "0 = (-5/4)x + (22/4)\r<BR>\n" );
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document.write( "subtract (22/4) from both sides of the equation to get:\r<BR>\n" );
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document.write( "-(22/4) = (-5/4)x\r<BR>\n" );
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document.write( "multiply both sides of the equation by (-4/5) to get:\r<BR>\n" );
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document.write( "-(4/5) * -(22/4) = x\r<BR>\n" );
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document.write( "multiplying these factors together, we get:\r<BR>\n" );
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document.write( "(-4 * -22) / (5*4) = x\r<BR>\n" );
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document.write( "we simplify this to get (88/20) = x\r<BR>\n" );
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document.write( "we simplify this further by dividing numerator and denominator of the fraction by 4 to get:\r<BR>\n" );
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document.write( "(22/5) = x\r<BR>\n" );
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document.write( "we commute this equation to get:\r<BR>\n" );
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document.write( "x = (22/5)\r<BR>\n" );
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document.write( "our coordinate pair for when y = 0 is going to be (x,y) = ((22/5),0).\r<BR>\n" );
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document.write( "we now have 2 points on the line.\r<BR>\n" );
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document.write( "we can find lots more points on the line by just setting x equal to some value and then solving for y.\r<BR>\n" );
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document.write( "the graph of this equation looks like this:\r<BR>\n" );
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document.write( "since (22/4) is equal to 5.5, then the coordinate pair of (0,(22/4)) is the same as (0,5.5) which is the intersection of the equation of the line with the y-axis which is also the value of y when x = 0.   the graph confirms this.\r<BR>\n" );
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document.write( "since (22/5) is equal to 4.4, then the coordinate pair of ((22/5),0) is the same as (4.4,0) which is the intersection of the equation of the line with the x-axis which is also the value of x when y = 0.   the graph confirms this.\r<BR>\n" );
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