EDGE Math 8

Graphs of Equations

The graph of an equation in two variables x and y is the set of all points $(x, y)$ on a plane that satisfies the equation. In the preceding example, the graph of the equation is the line shown in the figure.

Example

Which of the points $A (0, - 1)$ and $B (- 3, 10)$ is on the graph of the equation $y = 3 x - 1 ?$

Solution

To check if point $A (0, - 1)$ is on the graph of $y = 3 x - 1,$ substitute $x = 0$ and $y = - 1$ to the given equation. You will get the following:

Since the coordinates of point A make the equation true, point A is on the graph of $y = 3 x - 1.$ Point $B (- 3, 10)$ is not on the graph of $y = 3 x - 1$ since substituting $x = - 3$ and $y = 10$ to the equation yields a false statement, as shown below.