document.write( "Question 172946: Find the equation of a line that passes thru (3,7) and (2,-1) \n" ); document.write( "

Algebra.Com's Answer #127781 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Two points determine a line, so that's all you need
\n" ); document.write( "The general equation for a line is
\n" ); document.write( " $\"y+=+mx+%2B+b\"$
\n" ); document.write( "This looks like a single equation with 4 unknowns, and
\n" ); document.write( "that is unsolvable, but the 2 points given will allow
\n" ); document.write( "me to write 2 equations with 2 unknowns
\n" ); document.write( "given:
\n" ); document.write( "(3,7)
\n" ); document.write( "(2,-1)
\n" ); document.write( "(1) $\"7+=+m%2A3+%2B+b\"$
\n" ); document.write( "(2) $\"-1+=+m%2A2+%2B+b\"$
\n" ); document.write( "Now I solve for $\"m\"$ and $\"b\"$
\n" ); document.write( "First, subtract (2) from (1)
\n" ); document.write( " $\"8+=+m\"$
\n" ); document.write( "Now put this value for $\"m\"$ back into (1)
\n" ); document.write( " $\"7+=+8%2A3+%2B+b\"$
\n" ); document.write( " $\"b+=+7+-+24\"$
\n" ); document.write( " $\"b+=+-17\"$
\n" ); document.write( "The equation of the line that passes trough (3,7) and (2,-1) is
\n" ); document.write( " $\"y+=+8x+-+17\"$
\n" ); document.write( "Now check the answer
\n" ); document.write( "(3,7)
\n" ); document.write( " $\"7+=+8%2A3+-+17\"$
\n" ); document.write( " $\"7+=+24+-+17\"$
\n" ); document.write( " $\"7+=+7\"$
\n" ); document.write( "OK
\n" ); document.write( "(2,-1)
\n" ); document.write( " $\"-1+=+8%2A2+-+17\"$
\n" ); document.write( " $\"-1+=+16+-+17\"$
\n" ); document.write( " $\"-1+=+-1\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );