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# Equation of a Straight Line - Tutorial, Formula and Example

##### Definition

An equation that describes a straight line on 2D surface with x and y co-ordinates is the equation of straight line. The equation of straight line can be calculated using various equations :

• Slope Intercept Form
• Point Slope Form
• Two Point Slope Form
##### 1) Slope Intercept Form

As the name indicates, an equation which can be represented with the slope and slope intercept is calculated using the slope intercept form.

#### Formula :

Slope Intercept Form y = mx + c Where, m = Slope x = X Axis Points c = Y-intercept
###### Example :

Find the equation if slope is 4 and y-intercept is 7 Given, m = 4 and c = 7 Solution, y = mx + c y = 4x + 7 4x-y+7 = 0 is the equation of straight line.

##### 2) Point Slope Form

Equation of straight line formed by one co-ordinate point and slope is called as point slope form. It is expressed as

#### Formula :

(y - y1) = m(x- x1) Where, m = Slope x1 = X Axis Points y1 = Y Axis Points x, y = x and y Axis
###### Example :

Let slope be 7 and Co-ordinate point be (3,4), then Given, m = 7, x1 = 3 and y1 = 4 Solution, Step 1: Apply the values in (y - y1) = m(x- x1) (y-4) = 7 ( x-3) Step 2: Simplifying, (y-4) = 7x - 21 y-7x = -21 + 4 y-7x = -17 7x-y-17 = 0 is the equation.

###### 3) Two Point Slope Form

When two co-ordinate points are given, we can find straight line equation using two point slope form.

#### Formula :

(Y - Y1) / (Y2 - Y1) = (X - X1) / (X2 - X1) Where, m = Slope x1 = X Axis Points y1 = Y Axis Points x, y = x and y Axis
###### Example

Let consider the axis point (x1,y1) and (x2,y2) as (5,6) and (7,8), then Given, x1 = 5, y1 = 6, x2 = 7 and y2 = 8 Solution, (Y - 6) / (8 - 6) = (X - 5) / (7 - 5) (Y - 6) / 2 = (X - 5) / 2 (Y - 6) = (X - 5) x - y - 11 = 0

###### 4) Slope

Slope describes the steepness and direction of a straight line. We can find the slope when two co-ordinate points are given.

#### Formula :

m = (Y1 - Y2) / (X1 - X2) Where, m = Slope X1 , X2 = X Axis Points Y1, Y2 = Y Axis Points
###### Example :

Let consider the points (2,3) and (7,6). Given, x1 = 2, y1 = 3, x2 = 7 and y2 = 6 Solution, m = 3 - 6 / 2 - 7 m = -3 / -5 m = 3/5 = 0.6