Intercept Form

The intercept form of the line is the equation of the line segment based on the intercepts with both axes.

Intercept Form

Intercept Form Equation of a Line

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 flechas x = −4 = a.

If x = 0 flechas y = 2 = b.

Intercept Form

The intercept form is:

Intercept Form Calculations

The area is:

Intercept Form Calculations


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:

Intercept Form Calculations

The area of the triangle is:

Intercept Form Calculations

Solve the system:

Intercept Form Calculations

Intercept Form Calculations

Intercept Form Calculations

Intercept Form Calculations

Intercept Form Solution


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?