document.write( "Question 697404: Plans for a bridge are drawn on a coordinate grid. One girder of the bridge lies on the line y=6x+1. A perpendicular brace passes through the point (-4, 6). Write an equation of the line that contains the brace. \n" ); document.write( "

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Plans for a bridge are drawn on a coordinate grid. One girder of the bridge lies on the line y=6x+1. A perpendicular brace passes through the point (-4, 6). Write an equation of the line that contains the brace.
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document.write( "The red line is the line whose equation is \r\n" );
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document.write( "y = 6x + 1\r\n" );
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document.write( "We compare that to\r\n" );
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document.write( "y = mx + b\r\n" );
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document.write( "and see that the slope = m = 6. [b=1 means the y-intercept is \r\n" );
document.write( "(0,1) but we don't need that for this problem]\r\n" );
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document.write( "The green line is what we want the equation of\r\n" );
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document.write( "Since the green line is perpendicular to the red\r\n" );
document.write( "line, its slope is the negative reciprocal of\r\n" );
document.write( "the slope of the red.  That's 1 over 6 with the\r\n" );
document.write( "sign changed to negative, or .  And\r\n" );
document.write( "the green line goes through (-4,6).  So we use\r\n" );
document.write( "the point slope formula:\r\n" );
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document.write( "y - y₁ = m(x - x₁)\r\n" );
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document.write( "  y - 6 = [x - (-4)]\r\n" );
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document.write( "  y - 6 = (x + 4)\r\n" );
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document.write( "That's the equation in point-slope form.\r\n" );
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document.write( "If we want it in general equation, we multiply through\r\n" );
document.write( "by 6\r\n" );
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document.write( "6y - 36 = -1(x + 4)\r\n" );
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document.write( "6y - 36 = -x - 4\r\n" );
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document.write( " x + 6y = 32\r\n" );
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document.write( "If you want the slope-intercept form, solve it for y:\r\n" );
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document.write( "     6y = -x + 32\r\n" );
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document.write( "     6y = -1x + 32\r\n" );
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document.write( "Divide through by 6\r\n" );
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document.write( "     = x + \r\n" );
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document.write( "      y = x + \r\n" );
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document.write( "Edwin

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