Graphing Linear Equations
To graph a linear equation, you can create a table of values (x and y) and then simply connect the points with a line. It is good practice to choose both positive and negative x values. Choose an x value and then substiute the value in the equation to solve for y. This will give you the (x,y) point for the graph.
One strategy is to start at the y-int and then use the slope to determine the next point. Let's populate a table of values for \(y = 3x - 1\).
The y-int is at \(0,-1\) which gives us our first points.
| X | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| Y | -1 |
The slope is \(+3\) which means when x increases by 1, y increases by 3. Let's populate the table for \(x=1,2\):
| X | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| Y | -1 | 2 | 5 |
Finally, to populate the other values we decrease x by 1 and decrease y by 3.
| X | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| Y | -7 | -4 | -1 | 2 | 5 |
Finally, plot the points on a coordinates grid and connect them with a line. The line extends in both directions.
