document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132637>Question 1132637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The line y=-12/5 x+2 is exactly 3 units away from two other parallel to it. The distance, in units, between the y-intercepts of these two line is<BR>\n" );
document.write( "A)12 3/4 B)10 2/3 C)14 1/5 D)15 3/5 E)13 5/6 </SPAN>\n" );
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document.write( "By symmetry, the y-intercepts of the two lines will be the same distance from the y-intercept of the given line, 2.  So find the distance from y=2 to the y-intercept of one of the two lines and double that distance.<br><BR>\n" );
document.write( "Let A (0,2) be the y-intercept of the given line; let B(0,b) be the y-intercept of one of the two lines parallel to the given line and 3 units from it.<br><BR>\n" );
document.write( "Let C be the point on the given line that is 3 units from B.<br><BR>\n" );
document.write( "Then ACB is a right triangle.  Since the slope of the given line is -12/5, the ratio of the lengths of AC and BC is 12:5.  Since those are the legs of a right triangle, AB (the length we need to find) is the hypotenuse of a 5:12:13 right triangle.<br><BR>\n" );
document.write( "Then, since BC is the short leg of the triangle, AB is (13/5)*3 = 39/5 = 7.8.<br><BR>\n" );
document.write( "And so the distance between the y-intercepts of the two lines parallel to y = -12/5x+2 and 3 units from it is 2*7.8 = 15.6 = 15 3/5, answer D. </SPAN>\n" );
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