document.write( "Question 363034: Are the points (-1,8), (1,2), and (4,-7) on the same line? Explain your reasoning \n" ); document.write( "

Algebra.Com's Answer #258762 by Edwin McCravy(20086) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "First let's plot them to get a heuristic answer:\r\n" );
document.write( "\r\n" );
document.write( " (-1,8), (1,2), and (4,-7)\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Now let's get a ruler and see if they look like they are:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Yes they look like they do, but \"looking and seeing\" is not good enough\r\n" );
document.write( "for mathematical purposes.\r\n" );
document.write( "\r\n" );
document.write( "Another way, beside the way the other tutor showed you, to show it\r\n" );
document.write( "mathematically is to get the equation of the line through two of them and\r\n" );
document.write( "then to show that the third point satisfies the equation:\r\n" );
document.write( "\r\n" );
document.write( "We find the slope of the line that goes through  (-1,8) and (1,2):\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then we substitute in the point-slope formula:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we substitute the third point (4,-7) into that equation:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The third point, which was not used to find the equation of\r\n" );
document.write( "the line, satisfies the equation, so all three points lie on\r\n" );
document.write( "the same line.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );