Equation of the Line

An equation that defines a straight line is referred as the equation of the line. Finding equation of a line is very simple. We can find the equation of a line for the following conditions:

  • If the slope and  y intercept is given
  • If the slope and a point is given.
  • If two points on the line are given.

 

equation of the line

 

Finding the Equation of a Line if slope and y intercept is given:

 

  • The slope-intercept form of a line is y= mx + b,

              where m is the slope

                         b is the y-intercept.

 Example

 Find the equation of the line with slope -3 and y-intercept 5.

 Solution:                m = -3  and  b = 5


                The general equation is y = mx + b 

                Substitute the values into equation, we get 

                                                    y = -3x + 5

                      Hence,the equation of the line is y = -3x + 5

 

Check this topic Slope of a Line Equation it might be helpful to you for more help keep reading my blogs.

 

Finding the Equation of a Line if slope and a point is given:

 

Example:

Find the equation of a line if the slope is  -2 and passes through (6, 8)

Step 1: Use the slope-intercept form of a line: y = mx + b

                                          Given m = -2     Hence y = - 2x + b

Step 2 : Substitute values into equation:

        The y-intercept was not given. However, we are given the point, (6, 8). Thus x = 6 and y = 8
        Substitute the values to find  the y-intercept  b
                                                             y  =  mx + b
                                                             8  = -2(6) + b
                                                             8  = -12 + b
                                                            18 = b

Step 3: Solution

             Substituting the value of b, we get  y = -2x + 18

                 Hence,the equation of the line is y = -2x + 18

 

Finding the Equation of a Line passing through two given points:

 

Example:

Find the line that passes through (2, 4) and (6, 24)

Steps:

1)      Use the two points to find the slope using slope formula

2)      Use the slope and either one of the points to find the value the y-intercept.

Step 1:                       Slope          =   (y2– y1) / (x2 – x1)

                                                         =   (24– 4) / (6 – 2)

                                                         = 20/4 = 5

Step 2 :  Let’s choose the point (2,4)
                                                    y   =  mx + b
                                                    4  =  5(2) + b
                                                    4  = 10 + b
                                                    6 – 10 = b
                                                      -4 = b

Substituting the values in the general equation, we get

                                             y = -5x + 4

                  Hence the equation of the line is y = - 5x + 4