Question 547968: i have to solve the systems by graphing them i dont understand how to graph them . my equations are y=x-2 , y=4x + 1 can you explain how to graph them
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Your equations are linear equations. They represent the straight lines that are their graphs. You need just two points to determine a line. Then you just get a ruler (or anything with a straight edge) and draw a line connecting them.
The only question is what points to choose, and how to find them.
If you pick a value for x, you can calculate the corresponding y. You want to pick values that make the calculations easy, but that will also give you a good looking graph.
For  you could try
 (usually a good choice), and calculate  to get point (0,-2)
 would give you  and point (2,0)
For 
gives you  and point (0,1)
gives you  and point (2,9)
Then you plot the points with those x and y coordinates
 and then draw the lines 
With some luck, the graph may look good the first time, and you would see where the two lines cross.
(What I'm showing you is my second try. Adjustments are often necessary. Sometimes you realize that your points are too close to get a good line, or that they give you y values that are out of the graph you had started, or that the lines would cross beyond the edge of your graph. You may want to change some of your points, or you may want to change the scale on the x- and y-axes. Starting with a rough draft of your points and graph may be a good idea).
Your lines seem to cross at point (-1,-3). That is your solution, which can be expressed as point (-1,-3) or as x=-1 with y=-3.
However, it is common practice to verify by substituting  and  in your equations. If you are asked to show your work, do it.
For , substituting gives you  , showing that point (-1,-3) satisfies the equation and is on the line it represents.
For  , substituting gives you  , showing that point (-1,-3) satisfies the equation and is on the line it represents.
NOTE:
Verifying helps you catch mistakes. Besides, while in well designed classroom problems the answer will be what it looks, in real life problems, the solution could be close, but not exactly what the graph looks like.
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