document.write( "Question 81211: write the equation of the line passing through each of the given pairs of points. write result in slope-intercept form, where possible. \n" ); document.write( "
Algebra.Com's Answer #58204 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
write the equation of the line passing through each of the given pairs of points. write result in slope-intercept form, where possible.\r
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "You forgot to give the two points.\r\n" );
document.write( "Let's say they are these points:\r\n" );
document.write( "\r\n" );
document.write( "(-1, 3) and (4,-2)\r\n" );
document.write( "\r\n" );
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" );
document.write( "\r\n" );
document.write( "\"graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C5%2C++-x+%2B+2%29\"\r\n" );
document.write( "\r\n" );
document.write( "We see that it is not vertical. So we can proceed\r\n" );
document.write( "as usual:\r\n" );
document.write( "\r\n" );
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" );
document.write( "\r\n" );
document.write( "Use the slope formula:\r\n" );
document.write( "\r\n" );
document.write( "     y2 - y1\r\n" );
document.write( "m = —————————\r\n" );
document.write( "     x2 - x1\r\n" );
document.write( "\r\n" );
document.write( "where (x1, y1) = (-1,3) and (x2, y2) = (4, -2)\r\n" );
document.write( "\r\n" );
document.write( "    (-2) - (3)    -5      -5\r\n" );
document.write( "m = —————————— = ————— = ———— = -1\r\n" );
document.write( "    (4) - (-1)    4+1      5 \r\n" );
document.write( "\r\n" );
document.write( "Now substitute in the point slope formula:\r\n" );
document.write( "\r\n" );
document.write( "   y - y1 = m(x - x1)\r\n" );
document.write( "\r\n" );
document.write( "   y - 3 = (-1)(x - (-1) )\r\n" );
document.write( "\r\n" );
document.write( "   y - 3 = -(x + 1)\r\n" );
document.write( "\r\n" );
document.write( "   y - 3 = -x - 1\r\n" );
document.write( "\r\n" );
document.write( "       y = -x + 2\r\n" );
document.write( "\r\n" );
document.write( "That's the equation in the slope-intercept\r\n" );
document.write( "form because we can compare it with\r\n" );
document.write( "\r\n" );
document.write( "       y = mx + b\r\n" );
document.write( "\r\n" );
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" );
document.write( "  \r\n" );
document.write( "--------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "If the two points had been (4,-5) and (4,3)\r\n" );
document.write( "we would have gotten this vertical line:\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28300%2C300%2C+-5%2C5%2C-5%2C5%2C999%28x-4%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "and its equation would have simply been\r\n" );
document.write( "\r\n" );
document.write( "      x = 4\r\n" );
document.write( "\r\n" );
document.write( "because every point on it has 4 for \r\n" );
document.write( "its x-coordinate.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );