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Important Formulas: Linear Functions | The Complete SAT Course - Class 10 PDF Download

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−y= 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:

Important Formulas: Linear Functions | The Complete SAT Course - Class 10

2. Point-slope form:
Important Formulas: Linear Functions | The Complete SAT Course - Class 10

3. Standard form:
Important Formulas: Linear Functions | The Complete SAT Course - Class 10

4. Intercept form:
Important Formulas: Linear Functions | The Complete SAT Course - Class 10

Question for Important Formulas: Linear Functions
Try yourself:What is the slope (m) of a line passing through the points (2, 5) and (4, 9)?
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