document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=488297>Question 488297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I am trying to help my daughter with her Algebra and forgot how to solve for the following (y=mx+b) statement. I hope you can help as I have been out of this since my late twenties! \r<BR>\n" );
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document.write( "Write the slope-intercept form of an equation of the line that passes through the given point and is perpendicular to the equation given. <BR>\n" );
document.write( "(2,2), y= -1/5 x +5\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333338 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=333338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the slope intercept form of the equation of a straight line is y = mx + b<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y intercept<BR>\n" );
document.write( "the point you are given is:<BR>\n" );
document.write( "(x,y) = (2,2)<BR>\n" );
document.write( "the equation you are given is:<BR>\n" );
document.write( "y = (-1/5)x + 5<BR>\n" );
document.write( "the slope is (-1/5)<BR>\n" );
document.write( "the y intercept is 5<BR>\n" );
document.write( "the line perpendicular to this line will have a slope that is a negative reciprocal of the slope of this line.<BR>\n" );
document.write( "if the slope is a/b, then the negative reciprocal of the slope is -b/a<BR>\n" );
document.write( "since our slope is (-1/5), then the negative reciprocal is (5/1) which is equal to 5.<BR>\n" );
document.write( "the slope of our line is 5 and it passes through the point (2,2)<BR>\n" );
document.write( "the equation of our line will be y = mx + b<BR>\n" );
document.write( "we replace the m with 5 and we get:<BR>\n" );
document.write( "y = 5x + b<BR>\n" );
document.write( "to find b, we replace y with 2 and x with 2 and solve for b.<BR>\n" );
document.write( "this is because the point (x,y) = (2,2) which means that x = 2 and y = 2 at that point.<BR>\n" );
document.write( "we get:<BR>\n" );
document.write( "2 = 5*2 + b which becomes:<BR>\n" );
document.write( "2 = 10 + b<BR>\n" );
document.write( "subtract 10 from both sides of this equation to get:<BR>\n" );
document.write( "-8 = b which becomes:<BR>\n" );
document.write( "b = -8<BR>\n" );
document.write( "our equation becomes:<BR>\n" );
document.write( "y = 5x - 8<BR>\n" );
document.write( "a graph of both equations will show that our new equation is perpendicular to the original equation and will pass through the point (2,2).<BR>\n" );
document.write( "i have created a horizontal line at y = 2 and a vertical line at x = 2 in order to show you that our new line passes through that point.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-5%2C10%2C%28-1%2F5%29x+%2B+5%2C5x-8%2C2%2C100%28x-2%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-5%2C10%2C%28-1%2F5%29x+%2B+5%2C5x-8%2C2%2C100%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "for your additional information, the 2 lines will intersect at the point where the two equations are equal to each other.<BR>\n" );
document.write( "that point will be solved for below.<BR>\n" );
document.write( "the 2 equations are:<BR>\n" );
document.write( "y = (-1/5)x + 5<BR>\n" );
document.write( "y = 5x - 8<BR>\n" );
document.write( "we set both these equations equal to each other to get:<BR>\n" );
document.write( "(-1/5)x + 5 = 5x - 8<BR>\n" );
document.write( "add 8 to both sides of this equation to get:<BR>\n" );
document.write( "(-1/5)x + 13 = 5x<BR>\n" );
document.write( "add (1/5)x to both sides of this equation to get:<BR>\n" );
document.write( "13 = 5x + (1/5)x which becomes:<BR>\n" );
document.write( "13 = 26/5x<BR>\n" );
document.write( "that makes x = (5*13)/26 = 5/2)<BR>\n" );
document.write( "this is the same as x = 2.5<BR>\n" );
document.write( "we'll solve for y in both equations.<BR>\n" );
document.write( "the answers should be the same.<BR>\n" );
document.write( "y = -(1/5)x + 5 becomes y = -(1/5)*2.5 + 5 which becomes y = 4.5<BR>\n" );
document.write( "y = 5x - 8 becomes y = 5*2.5 - 8 which becomes y = 4.5<BR>\n" );
document.write( "we have our point of intersection of the 2 lines at x = 2.5 and y = 4.5<BR>\n" );
document.write( "this can be expressed as (x,y) = 2.5,4.5)<BR>\n" );
document.write( "the graph is shown below with the vertical and horizontal lines removed so you can see the intersection point easier.<BR>\n" );
document.write( "i also made the x and y axis symmetrical so you can see that the lines are really perpendicular to each other easier.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28-1%2F5%29x+%2B+5%2C5x-8%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28-1%2F5%29x+%2B+5%2C5x-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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