## What is the Equation of a Line?

The equation of a line describes its geometric properties and can be expressed in different forms. One of the most common forms of a linear equation is

- the slope-intercept form
- Another common form is the point-slope form
- Finally, the standard form of the equation of a line

There are three standard forms of the **equation of a line**:

**Slope-intercept form**

y = mx + b,

where m is the slope of the line and,

b is the y-intercept. This form is useful when you know the slope and y-intercept of the line.

**Point-slope form**

y – y1 = m(x – x1),

where (x1, y1) is a point on the line and

m is the slope of the line.

This form is useful when you know the slope of the line and one point that it passes through.

**Standard form**

Ax + By = C,

where A, B, and C are constants and

A is non-negative.

This form is useful when you need to compare the coefficients of two or more linear equations, or when you are working with linear programming or other optimization problems.

## How To Find the Equation of a Line?

To find the equation of a line given two points, you can use the **slope formula:**

m = (y2 – y1) / (x2 – x1)

Once you have the slope, you can use either the slope-intercept form or the point-slope form to write the equation of the line.

**For example,** let’s say we want to find the equation of the line passing through the points (2, 3) and (4, 5):

m = (5 – 3) / (4 – 2) = 1

Using the point-slope form with (2, 3) as our point, we get:

y – 3 = 1(x – 2)

Simplifying this equation gives us the slope-intercept form:

y = x + 1

So the equation of the line passing through the points (2, 3) and (4, 5) is y = x + 1.

## Straight Line Formulas

Formula Name | Formula |
---|---|

Slope Formula | m = (y2 – y1) / (x2 – x1) |

Point-Slope Formula | y – y1 = m(x – x1) |

Slope-Intercept Formula | y = mx + b |

Two-Point Formula | y – y1 = (y2 – y1) / (x2 – x1) (x – x1) |

Intercept Formula | x/a + y/b = 1 |

Distance Formula | d = |

Equation of a horizontal line | y = a or y=-a |

Equation of a vertical line | x=b or x=-b |

### Real life Examples of Straight Lines

- The edges of a piece of paper or a book
- The lines on a ruled notebook page
- The stripes on a flagpole
- The creases on a pair of pants
- The dashed lines on a road
- The straight sections of a railway track
- The lines on a graph paper
- The boundary lines on a basketball court or soccer field
- The edge of a wall or a building
- The seams on a piece of fabric.

### Examples of Straight Lines

- The line y = 2x – 3
- The line y = -4x + 7
- The line y = x
- The line x = 2
- The line y = 5
- The line x = -3
- The line y = -2x + 6
- The line y = 0
- The line x = 0
- The line y = -7