To find the intercepts of a linear equation, which is usually written as (Ax + By = C), you can follow these easy steps:

1. Y-Intercept:

• First, set (x = 0) in the equation.
• Then solve for (y):
  [By = C \implies y = \frac{C}{B}]
• This means the y-intercept is the point ((0, \frac{C}{B})).

2. X-Intercept:

• Now, set (y = 0) in the equation.
• Then solve for (x):
  [Ax = C \implies x = \frac{C}{A}]
• This means the x-intercept is the point ((\frac{C}{A}, 0)).

Example:

Let’s look at the equation (2x + 3y = 6):

• For the y-intercept, you will find it is ((0, 2)).
• For the x-intercept, it is ((3, 0)).

These intercepts, where the line crosses the axes, help us draw the graph of the equation easily.