document.write( "Question 78574: How do I write the equation of the line passing through each of the given pairs of points. And write my result in slope-intercept form, where possible for two problems?\r
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Algebra.Com's Answer #56374 by Edwin McCravy(20055)\"\" \"About 
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How do I write the equation of the line passing through each of the given pairs of points. And write my result in slope-intercept form, where possible for two problems?
\n" ); document.write( "1. (-1, 3) and (4,-2)
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document.write( "We first plot those two points and draw a line \r\n" );
document.write( "through them to find out if it is vertical or\r\n" );
document.write( "not. The equations of all lines can be placed\r\n" );
document.write( "in slope-intercept form except the equations\r\n" );
document.write( "for vertical lines. This is the graph we get:\r\n" );
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document.write( "\"graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C5%2C++-x+%2B+2%29\"\r\n" );
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document.write( "We see that it is not vertical. So we can proceed\r\n" );
document.write( "as usual:\r\n" );
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document.write( "We are to find an equation of the line containing \r\n" );
document.write( "the points (-1,3) and (4,-2)\r\n" );
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document.write( "Use the slope formula:\r\n" );
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document.write( "     y2 - y1\r\n" );
document.write( "m = —————————\r\n" );
document.write( "     x2 - x1\r\n" );
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document.write( "where (x1, y1) = (-1,3) and (x2, y2) = (4, -2)\r\n" );
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document.write( "    (-2) - (3)    -5      -5\r\n" );
document.write( "m = —————————— = ————— = ———— = -1\r\n" );
document.write( "    (4) - (-1)    4+1      5 \r\n" );
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document.write( "Now substitute in 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 - 3 = (-1)(x - (-1) )\r\n" );
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document.write( "   y - 3 = -(x + 1)\r\n" );
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document.write( "   y - 3 = -x - 1\r\n" );
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document.write( "       y = -x + 2\r\n" );
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document.write( "That's the equation in the slope-intercept\r\n" );
document.write( "form because we can compare it with\r\n" );
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document.write( "       y = mx + b\r\n" );
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document.write( "and see that its slope m is -1 and its\r\n" );
document.write( "y-intercept (0,b) is the point (0,2)\r\n" );
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\n" ); document.write( "2. (2,-3) and (2, 4)
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document.write( "As before we first plot those two points and \r\n" );
document.write( "draw a line through them to find out if it is\r\n" );
document.write( "vertical or not. The equations of all lines \r\n" );
document.write( "can be placed in slope-intercept form except\r\n" );
document.write( "the equations for vertical lines.\r\n" );
document.write( "This is the graph we get:\r\n" );
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document.write( "\"graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C5%2C+9999%28x-2%29%29\"\r\n" );
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document.write( "We see that it is vertical.  That means we\r\n" );
document.write( "cannot proceed as above to find its equation.\r\n" );
document.write( "However it is very easy because we see that\r\n" );
document.write( "every point on the vertical line is either\r\n" );
document.write( "directly above or directly below the point\r\n" );
document.write( "on the x-axis where x = 2,\r\n" );
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document.write( "So that's its equation:\r\n" );
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document.write( "     x = 2\r\n" );
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document.write( "[The equations of vertical lines are always\r\n" );
document.write( " of the simple form\r\n" );
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document.write( "     x = a\r\n" );
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document.write( "where a is the number on the x-axis where the\r\n" );
document.write( "vertical line cuts through at.]\r\n" );
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document.write( "Edwin
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