According to South Eastern Louisiana University, to solve for the x and y intercepts in a linear equation of the form y = mx + b, set one of the variables, either x or y depending on the desired intercept, equal to zero, and solve algebraically.
An example provided by SELU uses the equation 3x + 4y = 12. The first step they take is to set y = 0 and solve for the x intercept. The x intercept is the point on the x axis where y = 0. Replacing y with 0 yields 3x + 4(0) = 12. Since 4(0) = 0, the equation becomes 3x = 12. To get the x variable alone on the left side of the equation, divide each side by 3. The equation now appears as x = 12/3. Solving 12/3 provides the x intercept, x = 4.
Similarly, following SELU's provided example, to solve for the y-intercept, set x = 0, and solve algebraically. Replacing x for 0 in the original equation produces the equation 3(0) + 4y = 12. Since 3(0) = 0, the equation becomes 4y = 12. Dividing both sides by 4, yields y = 12/4, or y = 3.