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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!
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website!  is a linear equation. Its graph is a straight line.
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  and solving for  is often a good strategy. Making  and solving for  could work too.
For your equation:
Making results in  -->  -->  , giving you the pioint (0,-2) .
Making results in  -->  -->  , giving you the point (3,0).
With those two points I would draw the x-axis from -2 to 5 (to include , and , 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.
The slope and y-intercept can be seen from the graph, or can be "read" from the slope-intercept equation for the line.
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.
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  . 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.
There are infinite ways to write the equation for a line. You were giveen
, but the same line could be described by many equivalent equations:
 -->  -->  -->  and infinite more.
My favorite version is  . 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 .
In the slope-intercept form of the equation for the line, the number that multiplies the (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
you see that the slope is and the y-intercept is  , even if you do not graph the line.
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