Graphing Linear Equations
The graph of a linear equation in two variables is a line (that's why they call it linear ).
If you know an equation is linear, you can graph it by finding any two solutions
and ,
plotting these two points, and drawing the line connecting them.
Example 1:
Graph the equation .
You can find two solutions, corresponding to the -intercepts and -intercepts of the graph, by setting first and then .
When , we get:
When , we get:
So the two points are and .
Plot these two points and draw the line connecting them.
If the equation is in slope-intercept form or point-slope form , you can also use the slope to help you graph.
Example 2:
Graph the line .
From the equation, we know that the -intercept is , the point and the slope is . Graph the point and from there go up units and to the right unit and graph a second point. Draw the line that contains both points.
Horizontal and vertical lines have extra simple equations.
Example 3:
Horizontal line:
Vertical line: