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.

Example 1.

A line has an x-intercept of 5 and a y-intercept of 3. Find its equation.

Example 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:

Example 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:

Example 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?

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.