document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179087>Question 1179087</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the distance between two parallel lines <BR>\n" );
document.write( "Y=2x-1, y=2x+9<BR>\n" );
document.write( "I tried graphing it and finding the perpendicular intercept but my numbers are not coming out right. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #808578 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=808578\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The video referenced by the other tutor shows a perfectly good way of solving the problem:<BR>\n" );
document.write( "(1) Using the slopes of the given lines and y-intercept of the first line, find the equation of the line perpendicular to that first line containing that y-intercept;<BR>\n" );
document.write( "(2) use the equation of that perpendicular line and the equation of the second given line to find the point of intersection; and<BR>\n" );
document.write( "(3) use the distance formula with that point of intersection and the y-intercept of the first line to get the distance between the two lines.<br><BR>\n" );
document.write( "There is a lot of good math in that solution process; you should understand it and know how to use it.<br><BR>\n" );
document.write( "But there are much easier and faster ways to answer the problem.  Below are two of them.<br><BR>\n" );
document.write( "First alternative: Make a sketch with a right triangle<br><BR>\n" );
document.write( "Sketch a graph of the two lines with slope 2 and y-intercepts -1 and +9;<BR>\n" );
document.write( "Draw the perpendicular segment from (0,9) to the other line;<BR>\n" );
document.write( "Look at the right triangle whose sides are that perpendicular segment, part of the second line, and part of the y-axis.  Since the slopes of the two lines are 2, we can call the lengths of the two legs of that right triangle x and 2x; and the hypotenuse is 10.  Then from the Pythagorean Theorem,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%282x%29%5E2=10%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%282x%29%5E2=10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%5E2=100 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2=100 ALIGN=MIDDLE  ALT=\"5x%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=20 ALIGN=MIDDLE  ALT=\"x%5E2=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"x+=+2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: The distance between the two lines (the length of the perpendicular segment between the two lines) is x = 2*sqrt(5)<br><BR>\n" );
document.write( "Second alternative: Use the point-to-line distance formula<br><BR>\n" );
document.write( "A very useful formula to know is for finding the distance from a given point to a given line:<br><BR>\n" );
document.write( "Given the equation of a line in the form Ax+By+C=0 and a point (p,q), the distance from the point to the line is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%28Ap%2BBq%2BC%29%2F%28sqrt%28A%5E2%2BB%5E2%29%29%29 ALIGN=MIDDLE  ALT=\"abs%28%28Ap%2BBq%2BC%29%2F%28sqrt%28A%5E2%2BB%5E2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use the equation of the first line in the required form (2x-y-1=0) and the y-intercept of the second line (0,9) as the fixed point and plug the numbers into the formula:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%282%280%29-1%289%29-1%29%2F%28sqrt%282%5E2%2B1%5E2%29%29%29+=+abs%28%28-10%29%2Fsqrt%285%29%29+=+2%2Asqrt%285%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );