The points at which a graph crosses the coordinate axes are called the intercepts of the graph. The graph of the equation y = 3x + 2 crosses the y-axis at y = 2—that is, when x = 0, y = 2. All points on the y-axis have an x-coordinate of 0, so the equation for the y-axis is x = 0. In the same manner, all points on the x-axis have a y-coordinate of 0, so the equation for the x-axis is y = 0. The x-intercept for the line y = 3x + 2 can be found by setting y = 0 and solving for x to find that x = −2/3.
The x-intercept for the graph with equation 2x + 3y = 12 is found by setting y = 0 and solving for x. The x-intercept is 6. The y-intercept for 2x + 3y = 0 is found by setting x = 0 and solving to find that y = 4. You now know that the points (6, 0) and (0, 4) are two points on the graph of this equation, and you can use these two points to sketch a graph of the equation.
The graph of an equation that has degree 1 will always be a line. For that reason, equations of degree 1 are called linear equations.
Example: Find the intercepts for the equation 5x − 6y = 24, and use these results to find the slope of the line. Sketch a graph of the line.