3.2 Graphing Linear Equations in Two Variables

3. Method: Because two distinct points determine a line, to graph a linear equation,
plot any two distinct ordered pair solutions and connect them with a line. (Plot a
third solution as a check.)
4. Don't pick points to graph that are too close together. (It would be hard to graph
an accurate line.)
5. Intercepts:
a. The x-intercept is the point where the graph crosses the x-axis.
Find the x-intercept by plugging zero on for the y coordinate and solving
the resulting equation for x. (Let y = 0.)
b. The y-intercept is the point where the graph crosses the y-axis.
Find the y-intercept by plugging zero on for the x coordinate and solving
the resulting equation for y. (Let x = 0.)
6. Lines through the Origin: If A and B are non-zero real numbers, the graph of
a linear equation of the form
Ax + By = 0
passes through the origin (0, 0). (Thus, to graph this type of linear equation, plot
the point (0, 0), which is the x- and y- intercept, and two other points. The x- and
y-intercepts will not be enough to graph these lines.)
7. Horizontal Line: A linear equation of the form y = b (or By + C = 0 ) has a
graph given by a horizontal line through the point (0, b).
8. Vertical Line: A linear equation of the form x = a (or 1⋅ x + 0⋅ y = a) has a
graph given by a vertical line through the point (a, 0).
9. See the summary of linear equations on page 212.
10. You can graph linear equations of the form Ax + By = C in a calculator by
first solving for y. Enter the resulting expression into one of the slots in the y=
key. Hit the GRAPH key. Check that the window shows the x- and y-intercepts.
If these intercepts do not show in the window, go to the WINDOW key and
change the x and y ranges. (The Standard window - #6 ZStandard in the ZOOM
key is often a place to start.)