document.write( "Question 701518: please help me solve this problem: \"write the equation of a line that passes through (21,-40) and has a slope of 4/5\" i need to find the equation of the line \n" ); document.write( "

Algebra.Com's Answer #432525 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
If you know the $\"highlight%28slope%29\"$ , m, and the coordinates of a $\"highlight%28point%29\"$ , (a,b),
\n" ); document.write( "the equation of the line can be written as
\n" ); document.write( " $\"y-b=m%28x-a%29\"$
\n" ); document.write( "That is called the $\"highlight%28point%29\"$ - $\"highlight%28slope%29\"$ form of the equation of the line.
\n" ); document.write( "It is derived from the definition of $\"highlight%28slope%29\"$
\n" ); document.write( "as the difference in y-coordinates divided by
\n" ); document.write( "difference in x-coordinates for any pair of points on the line.
\n" ); document.write( "For any unknown point (x,y) and a known point (a,b),
\n" ); document.write( "their coordinates and the slope, m, are related by
\n" ); document.write( " $\"%28y-b%29%2F%28x-a%29=m\"$ --> $\"y-b=m%28x-a%29\"$
\n" ); document.write( "
\n" ); document.write( "For your problem,
\n" ); document.write( " $\"y-%28-40%29=%284%2F5%29%28x-21%29\"$ --> $\"highlight%28y%2B40=%284%2F5%29%28x-21%29%29\"$
\n" ); document.write( "That is one of the infinite number of equivalent equations for the line.
\n" ); document.write( "It can be transformed into the unique slope-intercept form of the equation for the line.
\n" ); document.write( " $\"y%2B40=%284%2F5%29%28x-21%29\"$ --> $\"y%2B40=%284%2F5%29x-21%284%2F5%29\"$ --> $\"y%2B40=%284%2F5%29x-84%2F5\"$ --> $\"y=%284%2F5%29x-84%2F5-40\"$ --> $\"y=%284%2F5%29x-84%2F5-200%2F5\"$ --> $\"highlight%28y=%284%2F5%29x-284%2F5%29\"$ (in slope-intercept form) \n" ); document.write( "

\n" );