1.9: Coordinate Plane, Graphs of Equations
The Coordinate Plane
The coordinate plane describes where a point is in two dimensional space.
Here is an example:
Note:
- The $x$-axis and $y$-axis are real number lines, oriented perpendicularly. They intersect at the origin $(0,0)$.
- A coordinate $(x, y)$ means to move left/right $x$ units from the origin, and up/down $y$ units.
- The $x$- and $y$-axis divide up space into quadrants, which are labeled I, II, III and IV above.
Plot the points $(-1, 2), (-2, -4), (3, -1), (1, 1)$.
Graphs of Equations
Consider $2x - y = 3$.
If $x = 2$ and $y = 1$, then the equation is true. You can represent this as a coordinate $(2, 1)$.
But $(4, 5)$ works as well. In fact, there are infinite possibilities.
These possibilities are called the graph.
A graph of an equation in $x$ and $y$ is all points $(x, y)$ which make the equation true.
Sketch the graph of $2x - y = 3$ in the coordinate plane.
Sketch the graph of $y = x^2 - 2$ in the coordinate plane.
Sketch the graph of $y = \lvert x \rvert$ in the coordinate plane.
Intercepts
The $x$-intercept of a graph is the $x$-coordinate where the graph intersects the $x$-axis.
The $y$-intercept of a graph is the $y$-coordinate where the graph intersects the $y$-axis.
The $y$-intercept of a graph is the $y$-coordinate where the graph intersects the $y$-axis.
To find all $x$-intercepts, set $y = 0$ and solve for $x$.
To find all $y$-intercepts, set $x = 0$ and solve for $y$.
Given $y = x^2 - 2$, find all $x$- and $y$-intercepts.