# POINT SLOPE FORM EQUATION OF A LINE

## About "Point slope form equation of a line"

"Point slope form equation of a line" is one of the ways to express the equation of a line.

Here, we will form equation of a straight line using the given point and slope.

Point slope form equation of a line

Here,

Slope of the line  =  m

Point  =  (x₁ , y)

## Point slope form equation of a line - Practice problems

Problem 1 :

Find the general equation of the straight line passing through the point (-2,3) with slope 1/3.

Solution :

Given : Point  =  (-2, 3)  and  slope  m  =  1/3

So, the equation of the straight line in point-slope form is

y - y = m(x - x)

Plugging (x₁ , y₁) = (-2 , 3) and m = 1/3, we get

y - 3 = (1/3)(x + 2) ----------> 3y - 9 = x + 2

3y - 9 = x + 2 ------------> 0 = x - 3y + 11

Hence the general equation of straight line is x - 3y + 11 = 0

Problem 2 :

Find the general equation of the straight line passing through the point (1, 2) with slope -4.

Solution :

Given : Point  =  (1, 2)  and  slope  m  =  -4

So, the equation of the straight line in point-slope form is

y - y = m(x - x)

Plugging (x₁ , y₁) = (1 , 2) and m = -4, we get

y - 2 = -4(x - 1) -----> y - 2 = -4x + 4 -----> 4x + y - 6  =  0

Hence the general equation of straight line is 4x + y - 6 = 0

Problem 3 :

Find the general equation of the straight line passing through the point (5, -4) with slope 2/3.

Solution :

Given : Point  =  (5, -4)  and  slope  m  =  2/3

So, the equation of the straight line in point-slope form is

y - y = m(x - x)

Plugging (x₁ , y₁) = (5 , -4) and m = 2/3, we get

y + 4 = (2/3)(x - 5) -----> 3y + 12 = 2x - 10 -----> 2x - 3y - 22 = 0

Hence the general equation of straight line is 2x - 3y - 22 = 0

## Other forms of equation of a straight line

Apart from point slope form equation of a straight line, we have some other different forms of equation of a straight line.

They are

(i)  Slope intercept form

(ii) Two points form

(iii) Intercept form.

Let us look at the above different forms of equation of a straight line in detail.

## Slope intercept form

Here,

Slope of the line  =  m

y-intercept  =  b

## Two points form

Here, the two points are

(x₁ , y) and (x₂ , y)

## Intercept form

Here,

x- intercept  =  a

y- intercept  =  b

Apart from the above forms of equation of straight line, there are some other ways to get equation of a straight line.

1. If a straight line is passing through a point (0,k) on y-axis and parallel to x-axis, then  the equation of the straight line is   y = k

2. If a straight line is passing through a point (c,0) on x-axis and parallel to y-axis, then  the equation of the straight line is   x = c

3. Equation of x-axis is  y  =  0.

(Because, the value of "y" in all the points  on x-axis is zero)

4. Equation of y-axis is  x  =  0.

(Because, the value of "x" in all the points  on y-axis is zero)

5. General equation of a straight line is

ax + by + c  =  0

After having gone through above stuff, we hope that students would have understood the stuff "Point slope form equation of a line".

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