Point Slope Form

Point Slope Form

Equation of a straight line in terms of its slope (m) and a point (x1, y1) through which it passes is called the point slope form equation. It is written as

                    y – y= m(x – x1)

To derive this equation, let us suppose a straight line AB whose slope is m and passes through the point C (x1, y1). If P (x, y) be any point on the line AB, then                   

Slope of CP

                    But slope of AB = m

Since AB and CP represents the same line,

                    Slope of line AB = Slope of CP

Slope of line AB = Slope of CP

   or,      y – y1 = m(x – x1)

which is the required equation in point slope form.


Corollary: If the straight line passes through the two given points (x1, y1) and (x2, y2) then its slope can be obtained by                 

Slope (m)

        And hence the equation of the line can be obtained by the formula,

                    y – y1 = m (x – x1)

two point form equation

This is called two point form equation.

 

Workout Examples

Example 1: Find the equation of a straight line passing through the point (3, 2) and having the slope equal to 3/5.

Solution: Here,

                   Slope (m) = 3/5

                   Point = (3, 2)

                   x1 = 3    and    y1 = 2

          The equation of the line is,

                   y – y1 = m(x – x1)

          i.e.     y – 2 = 3/5 (x – 3)

          or,     3(x – 3) = 5(y – 2)

          or,     3x – 9 = 5y – 10

          or,     3x – 5y – 9 + 10 = 0

          or,     3x – 5y + 1 = 0

          Which is the required equation of the line.

 

Example 2: Find the equation of a straight line passing through the point (-2, 3) and having an angle of inclination 60° with x-axis.

Solution: Here,

                   Angle of inclination (θ) = 60°

                   Slope (m) = tanθ = tan60° = √3

                   Point = (–2, 3)

                   x1 = –2     and     y1 = 3

          The equation of the line is,

                   y – y1 = m(x – x1)

          i.e.     y – 3 = √3(x + 2)

          or,     √3(x + 2) = y – 3

          or,     √3x + 2√3 – y + 3 = 0

          or,     √3x – y + 3 + 2√3 = 0

          or,     3x – 5y + 1 = 0

          Which is the required equation of the line.

 

Example 3: Find the equation of a straight line passing through the points (-2, 3) and (2, 4).

Solution: Here,

                   The given points are (-2, 3) and (2, 4)

                   x1 = –2     and      y1 = 3

                     x2 = 2       and      y2 = 4

          The equation of the line is,

two point form equation

           or,     x + 2 = 4(y – 3)

           or,     x + 2 = 4y – 12

           or,     x – 4y + 2 + 12 = 0

           or,     x – 4y + 14 = 0

           Which is the required equation of the line.

 

You can comment your questions or problems regarding the point slope form equation here.


No comments:

Powered by Blogger.