document.write( "Question 144233: the line of an equation with a slope of 2/3 goes through the point (3,5). What is the y-coordinate of the point the line goes through when x=6 \n" ); document.write( "

Algebra.Com's Answer #105000 by SRCCE(1) $\"\"$ $\"About$

You can put this solution on YOUR website!
We first need to write the equation of the line with slope 2/3 and that goes through the point (3,5). To do this, we need to find the y-intercept. Using the point-slope form of a linear equation, \r
\n" ); document.write( "\n" ); document.write( "y - y1 = m * (x - x1), substituting (x1, y1) with (3,5) and m with 2/3\r
\n" ); document.write( "\n" ); document.write( "y - 5 = 2/3 (x - 3). \r
\n" ); document.write( "\n" ); document.write( "Now we have to simplify it, using the distributive property on the right side of the equal sign:\r
\n" ); document.write( "\n" ); document.write( "y - 5 = 2/3 x - 2. (Remember 2/3 * 3 = 2)\r
\n" ); document.write( "\n" ); document.write( "Add 5 to both sides of the equal sign.\r
\n" ); document.write( "\n" ); document.write( "y - 5 + 5 = 2/3 x - 2 + 5\r
\n" ); document.write( "\n" ); document.write( "And simplify\r
\n" ); document.write( "\n" ); document.write( "y = 2/3 x + 3.\r
\n" ); document.write( "\n" ); document.write( "Now we have to find the y-coordinate of the point on the line when x = 6. Substitute 6 for x in the above equation.\r
\n" ); document.write( "\n" ); document.write( "y = (2/3) (6) + 3
\n" ); document.write( "y = 4 + 3
\n" ); document.write( "y = 7.\r
\n" ); document.write( "\n" ); document.write( "So the y-coordinate of the point the line goes through when x = 6 is 7.
\n" ); document.write( " \n" ); document.write( "

\n" );