Question 869761: I need help with graphing linear equations in 2 variables
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Linear equations, like  , or  or 
graph as straight lines. (That is why they are called "linear").
Since two points determine a line, to graph a linear equation you just need to plot two points
(two (x,y) pairs) and connect them with a straight line.
One point and a slope can also be a useful cambination.
That sounds easy, but finding points that are
easy to calculate and
conveniently located is not always easy.
Vertical lines, like are easy to graph,
and so are horizontal lines like .
Slanted lines may be easy or harder to graph.
Take .
You can make  and  and get two helpful points:
For ,  --> --> gives you point (0,2).
For ,  gives you point (4,0).
You plot those two points; connect them, and you got your line.
A linear equation like  makes graphing more complicated.
You could do as above and find points (7/3,0) and (0,-7/5),
but those points are hard to locate precisely.
Sometimes points are hard to calculate;
sometimes they are hard to locate,
and sometimes the two points you get are too close together to draw the line accurately.
In that case, you try, try again.
Practice will tell you what to do next time.
For , I would solve for  to get something like this:
--> --> <--> .
Leaving the equation as helps me figure out a good integer  value,
that will give me an integer value.
For ,  and  .
That gives me point (4,1).
For  ,  and  .
That gives me point (-1,-2).
With those two points, I can draw the line.
However, with just one of those points, and the  slope, I can get other points without calculating.
A slope of means that as increases by  ,  .
That means that from any point, adding to the and  to the I get another point.
From (4,1), I get (4+5,1+3) = (9,4),
and adding again I get (9+5,4+3) = (14,7).
I could subtract instead of adding, and get (4-5,1-3) = (-1,-2).
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