Important Formulas: Linear Functions

Linear Function Formula

A linear equation is an equation in which every term is either just a constant or the product of a constant and a variable of exponent 1. A function is a relation in which every input has exactly one output. Every linear equation represents a line. All lines except vertical lines are functions. Let us learn linear function formulas along with a few solved examples.

What are Linear Function Formulas?

There are multiple linear function formulas to find the equation of a line depending on the available information. Linear function formulas are applicable to find the equation of any line except vertical line as vertical line is NOT a function.
The linear function formulas are:

• y = mx + b (slope-intercept form)
• y - y₁ = m (x - x₁) y-y₁ = m(x-x₁) (point-slope form)
• Ax + By = C (standard form)
• x/a + y/b = 1 (intercept form)

Here,

• (x, y) in every equation is a general point on the line.
• ( x₁, y₁) (x₁,y₁) is any fixed point on the line.
• m is the slope of the line. It can be defined as Rise/Run (or) y₂ - y₁/x₂ - x₁ where ( x₁, y₁) (x₁, y₁) and (x₂, y₂) (x₂, y₂) are any two points on the line.
• (a, 0) and (0, b) are the x-intercept and y-intercept respectively.
• A, B, and C are constants.

Linear Function Formulas

1. Slope-intercept form:

2. Point-slope form:

3. Standard form:

4. Intercept form: