document.write( "Question 559100: I have to find the slope and y-intercept of my equations. I cannot figure out how to graph it and I'm a little confused about solving the equations. One of the problems is 3y+6=2x Please help, thanks! \n" ); document.write( "

Algebra.Com's Answer #363309 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"3y%2B6=2x\"$ is a linear equation. Its graph is a straight line.
\n" ); document.write( "To graph it you just need to find and plot two points, and then connect them with a straight line. Chosing the points is an art, and practice improves your artistic ability. Making $\"x=0\"$ and solving for $\"y\"$ is often a good strategy. Making $\"y=0\"$ and solving for $\"x\"$ could work too.
\n" ); document.write( "For your equation:
\n" ); document.write( "Making $\"x=0\"$ results in $\"3y%2B6=0\"$ --> $\"3y=-6\"$ --> $\"y=-2\"$ , giving you the pioint (0,-2) .
\n" ); document.write( "Making $\"y=0\"$ results in $\"0%2B6=2x\"$ --> $\"2x=6\"$ --> $\"x=3\"$ , giving you the point (3,0).
\n" ); document.write( "With those two points I would draw the x-axis from -2 to 5 (to include $\"x=0\"$ , and $\"x=3\"$ , and a little beyond on both sides). I would draw the y-axis from -4 to 2 for similar reasons. You could use wider ranges on both axes too.
\n" ); document.write( "The slope and y-intercept can be seen from the graph, or can be \"read\" from the slope-intercept equation for the line.
\n" ); document.write( "In the graph, you see the point where the line crosses (intercepts) the y-axis. It's (0,-2). The x-coordinate of the point where the line crosses the y- axis is always zero, of course. The y-coordinate is what we want to know, and that value is what we call the y-intercept.
\n" ); document.write( "You can also see from the graph that to go from (0,-2) to (3,0) you run 3 spaces to the right and rise 2 spaces straight up. The slope is the ratio of that rise, divided by that run, or $\"2%2F3\"$ . You can calculate it from any 2 points in the graph. For a straight line, it will always be the same, whatever points you chose.
\n" ); document.write( "There are infinite ways to write the equation for a line. You were giveen
\n" ); document.write( " $\"3y%2B6=2x\"$ , but the same line could be described by many equivalent equations:
\n" ); document.write( " $\"3y%2B6=2x%7D%7D+--%3E+%7B%7B%7B2x-3y-6=0\"$ --> $\"2x-3y=6\"$ --> $\"4x-6y=12\"$ --> $\"20x-30y=60\"$ and infinite more.
\n" ); document.write( "My favorite version is $\"y=%282%2F3%29x-2\"$ . That is called the slope-intercept form. There are many ways to write the equation for a line, but there is only one slope-intercept form for each line. To find it, you just solve for $\"y\"$ .
\n" ); document.write( "In the slope-intercept form of the equation for the line, the number that multiplies the $\"x\"$ (with a minus sign if there is one) is the slope, and the other term (with a minus sign if there is one) is the y-intercept. In
\n" ); document.write( " $\"y=%282%2F3%29x-2\"$ you see that the slope is $\"2%2F3\"$ and the y-intercept is $\"-2\"$ , even if you do not graph the line. \n" ); document.write( "

\n" );