document.write( "Question 1126175: How do you write an equation of the line containing the given point and parallel to the given line? (5,-9); 6x-5y=7 \n" ); document.write( "

Algebra.Com's Answer #742488 by ikleyn(52864) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "In order for the line under the question be parallel to the given line  6x - 5y = 7,\r\n" );
document.write( "\r\n" );
document.write( "the left side of its equation must be exactly the same  6x - 5y = something.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "For now, I will write this equation in the form\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    6x - 5y = c,    (*)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where \"c\" is the constant term, now unknown to us.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To find its value, use the condition that the line contains the point (5,-9).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It means that the equation (*) must be satisfied when the values of the point coordinate  x= 5  and  y= -9  are substituted \r\n" );
document.write( "\r\n" );
document.write( "into the equation.  It gives\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "   6*5 - 5*(-9) = c = 30 + 45 = 75.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, you found the value of \"c\" :  c = 75,  and now your equation (*)  becomes\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    6x - 5y = 75.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "There are many closely relevant lessons in this site\r
\n" ); document.write( "\n" ); document.write( "    - Find the slope of a straight line in a coordinate plane passing through two given points\r
\n" ); document.write( "\n" ); document.write( "    - Equation for a straight line having a given slope and passing through a given point\r
\n" ); document.write( "\n" ); document.write( "    - Solving problems related to the slope of a straight line\r
\n" ); document.write( "\n" ); document.write( "    - Equation for a straight line in a coordinate plane passing through two given points\r
\n" ); document.write( "\n" ); document.write( "    - Equation for a straight line parallel to a given line and passing through a given point (*)\r
\n" ); document.write( "\n" ); document.write( "    - Equation for a straight line perpendicular to a given line and passing through a given point \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The most relevant lesson marked (*) in the list.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "These lessons are written specially for you.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Read them attentively and become an expert in the area.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );