Intercept Form
The intercept form of the line is the equation of the line segment based on the intercepts with both axes.
a is the x-intercept.
b is the y-intercept.
a and b must be nonzero.
The values of a and b can be obtained from the general form equation.
If y = 0, x = a.
If x = 0, y = b.
A line does not have an intercept form equation in the following cases:
1.A line parallel to the x-axis, which has the equation y = k.
2.A line parallel to the x-axis, which has the equation x = k.
3.A line that passes through the origin, which has equation y = mx.
Examples
1. A line has an x-intercept of 5 and a y-intercept of 3. Find its equation.
2.The line x − y + 4 = 0 forms a triangle with the axes. Determine the area of the triangle.
The line forms a right triangle with the origin and its legs are the axes.
If y = 0 
x = −4 = a.
If x = 0 y = 2 = b.
The intercept form is:
The area is:
3.A line passes through the point A = (1, 5) and creates a triangle of 18 u² with the axes. Determine the equation of the line.
Apply the intercept form:
The area of the triangle is:
Solve the system:
4.A line forms a triangle with the axes where the length of the leg formed by the x-axis is twice the length of the leg formed by the y-axis. If the line passes through the point A = (3, 2), what is its equation?
