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

english Calculators and Converters

Ask a Question