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Find the equation of the line passing through the points calculator

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The general equation of a straight line can be written as y = mx + c where m is the slope and c is the y-intercept.

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Answer: The equation of a line passing through the points (2, 3) and (4, 6) is 3x - 2y = 0

Let us proceed step by step to find the equation of the line.

Explanation:

Let us consider the given points (2, 3) and (4, 6).

As we know that the equation of a line passing through the points (x1, y1) and (x2, y2) is given by y - y1 = m (x - x1).

Here, m is the slope given by the formula m = (y2 - y1) / (x2 - x1)

Try using Cuemath's Slope Calculator that helps you to calculate the slope in a few seconds.

Hence on substituting the given points in the equation of a line, we get

y - 3 = m (x - 2)

m =  (y2 - y1) / (x2 - x1)

m = (6 - 3) / (4 - 2)

m = 3 / 2

Substituting value of m in y - 3 = m (x - 2), we get

⇒ y - 3 = 3 / 2 ( x - 2 )

⇒ 2y - 6 = 3x - 6

⇒ 2y - 3x = 0

⇒ 3x - 2y = 0

You can use Cuemath's online Equation of Line calculator to find the equation of line.

Therefore, the equation of a line passing through the points (2, 3) and (4, 6) is 3x - 2y = 0

Home > Geometry calculators > Coordinate Geometry > Equation of line passing through a given point and perpendicular to the line passing given points calculator

Method and examples
Equation of line passing through a given point and perpendicular to the line passing given points
 
Method  

1.1 Distance, Slope of two points

1. Find distance between the two points `A(7,8)` and `B(1,0)`

2. Find slope of the line joining two points `A(7,8)` and `B(1,0)`


A ( , ) , B ( , )
   

  1. `A(7,8),B(1,0)`
  2. `A(2,5),B(8,5)`
  3. `A(1,2),B(-3,5)`
  4. `A(-2,0),B(4,8)`
  5. `A(-2,0),B(-8,8)`
  6. `A(5,1),B(1,-2)`
  7. `A(6,4),B(-1,5)`
  8. `A(2,3),B(7,6)`
  9. `A(-3,4),B(5,-6)`
  10. `A(0,7),B(5,-2)`
  11. `A(0,0),B(-4,-6)`
  12. `A(3,5),B(6,4)`

 
1.2 Find the value of x or y

3. If distance between A(1,x) and B(-3,5) is 5, find the value of x.

Distance = , A ( , ) , B ( , )
 

  1. `distance=5`, `A(7,8),B(x,0)`
  2. `distance=5`, `A(1,x),B(-3,5)`
  3. `distance=10`, `A(x,0),B(4,8)`
  4. `distance=10`, `A(-2,x),B(-8,8)`
  5. `distance=5`, `A(5,1),B(x,-2)`
  6. `distance=6`, `A(6,x),B(-1,5)`
  7. `distance=7`, `A(2,x),B(7,6)`

 

4. If slope of A(-2,x) and B(5,-7) is -1, find the value of x.

Slope = , A ( , ) , B ( , )
 

  1. `slope=1.33`,`A(7,8),B(x,0)`
  2. `slope=-1`,`A(-2,x),B(5,-7)`
  3. `slope=3/5`,`A(2,3),B(x,6)`
  4. `slope=-5/4`,`A(-3,4),B(5,x)`
  5. `slope=-9/5`,`A(0,x),B(5,-2)`
  6. `slope=3/2`,`A(x,0),B(-4,-6)`

2. Points are Collinear or Triangle or Quadrilateral form

Find `A(0,0), B(2,2), C(0,4), D(-2,2)` are vertices of a square or not


A ( , ) , B ( , ) , C ( , ) , D ( , )
Find  
 

  1. `A(-1,-1),B(1,5)``,C(2,8)` are vertices of are collinear points (ABC)
  2. `A(0,-1),B(3,5)``,C(5,9)` are vertices of are collinear points (ABC)
  3. `A(2,8),B(1,5)``,C(0,2)` are vertices of are collinear points (ABC)
  4. `A(0,0),B(0,3)``,C(4,0)` are vertices of a right angle triangle (ABC)
  5. `A(-2,-2),B(-1,2)``,C(3,1)` are vertices of a right angle triangle (ABC)
  6. `A(-3,2),B(1,2)``,C(-3,5)` are vertices of a right angle triangle (ABC)
  7. `A(2,5),B(8,5)``,C(5,10.196152)` are vertices of an equilateral triangle (ABC)
  8. `A(2,2),B(-2,4)``,C(2,6)` are vertices of an isosceless triangle (ABC)
  9. `A(0,0),B(2,0)``,C(-4,0)``,D(-2,0)` are vertices of are collinear points (ABCD)
  10. `A(2,3),B(7,4)``,C(8,7)``,D(3,6)` are vertices of a parallelogram (ABCD)
  11. `A(1,5),B(1,4)``,C(-1,3)``,D(-1,4)` are vertices of a parallelogram (ABCD)
  12. `A(1,-1),B(-2,2)``,C(4,8)``,D(7,5)` are vertices of a rectangle (ABCD)
  13. `A(0,-4),B(6,2)``,C(3,5)``,D(-3,-1)` are vertices of a rectangle (ABCD)
  14. `A(3,0),B(4,5)``,C(-1,4)``,D(-2,-1)` are vertices of a rhombus (ABCD)
  15. `A(3,2),B(5,4)``,C(3,6)``,D(1,4)` are vertices of a square (ABCD)
  16. `A(0,0),B(2,2)``,C(0,4)``,D(-2,2)` are vertices of a square (ABCD)

3. Find Ratio

1. Find ratio of line joining A(5,12) and B(2,9) is divided by a point P(3,10)

A ( , ) , B ( , ) , P ( , )
 

  1. `A(1,-3),B(3,5),P(6,17)`
  2. `A(2,8),B(6,14),P(12,23)`
  3. `A(5,12),B(2,9),P(3,10)`
  4. `A(5,13),B(1,4),P(17/5,47/5)`

 

2. Find a point which divides the line joining A(-4,1) and B(17,10) in the ratio 1:2

A ( , ) , B ( , ) , ratio = : , Externally
 

  1. `A(5,13),B(1,4),m:n=2:3`
  2. `A(-4,1),B(17,10),m:n=1:2`
  3. `A(5,12),B(2,9),m:n=2:1`
  4. `A(2,8),B(6,14),m:n=5:3` Externally
  5. `A(1,-3),B(3,5),m:n=5:3` Externally

 

3. Find the ratio in which the x-axis divides the join of `A(2,1)` and `B(7,6)`? Also find the coordinates of the point of intersection.

A ( , ) , B ( , ) , divided by
 

  1. `A(2,1),B(7,6)` divided by x-axis
  2. `A(2,-4),B(-3,6)` divided by x-axis
  3. `A(2,-4),B(-3,6)` divided by y-axis

 

4. Find the ratio in which the point `P(x,4)` divides the join of `A(2,1)` and `B(7,6)`? Also find the value of `x`.

P ( , ) , A ( , ) , B ( , ) ,
 

  1. `P(x,4),A(2,1),B(7,6)`
  2. `P(x,0),A(2,-4),B(-3,6)`
  3. `P(0,y),A(2,-4),B(-3,6)`

4. Find Midpoint or Trisection points or equidistant points on X-Y axis

1. Find the midpoint of line joining points `A(-2,3)` and `B(5,4)`

2. Find the trisection points of line joining points `A(-2,3)` and `B(5,4)`

3. Find the point on the x-axis which is equidistant from `A(-2,3)` and `B(5,4)`

4. Find the point on the y-axis which is equidistant from `A(-2,3)` and `B(5,4)`


A ( , ) , B ( , )
 
       

  1. `A(-4,1),B(17,10)`
  2. `A(-2,3),B(5,4)`
  3. `A(-3,4),B(5,-6)`
  4. `A(0,7),B(5,-2)`
  5. `A(0,0),B(-4,-6)`
  6. `A(3,5),B(6,4)`

5. Find Centroid, Circumcenter, Area of a triangle

1. Find the centroid of a triangle whose vertices are `A(4,1),B(-2,-3),C(6,7)`

2. Find the circumcentre of a triangle whose vertices are `A(4,1),B(-2,-3),C(6,7)`

3. Find the area of a triangle whose vertices are `A(4,1),B(-2,-3),C(6,7)`

4. Find `A(4,1),B(-2,-3),C(6,7)` are collinear points or not (using area finding method)


A ( , ) , B ( , ) , C ( , )
 
       

  1. `A(2,5),B(4,9),C(6,4)`
  2. `A(-1,-1),B(1,5),C(2,8)`
  3. `A(-3,2),B(1,2),C(-3,5)`
  4. `A(0,-1),B(3,5),C(5,9)`
  5. `A(4,1),B(-2,-3),C(6,7)`

6. Find the equation of a line using slope, point, X-intercept, Y-intercept

1. Find the equation of a line passing through point `A(5,4)` and having slope `1/2`

A ( , ) ; Slope :
 

  1. slope`=2`,`A(0,3)`
  2. slope`=1/4`,`A(0,0)`
  3. slope`=1/2`,`A(5,4)`

 

2. Find the equation of a line passing through two points `A(3,5)` and `B(6,4)`

A ( , ) , B ( , )
 

  1. `A(7,8),B(1,0)`
  2. `A(6,4),B(-1,5)`
  3. `A(2,3),B(7,6)`
  4. `A(-3,4),B(5,-6)`
  5. `A(0,7),B(5,-2)`
  6. `A(0,0),B(-4,-6)`
  7. `A(3,5),B(6,4)`

 

3. Find the equation of a line having slope = 2 and Y-intercept = 3

Slope : ; Y-intercept :
 

  1. slope`=1/2`,Y-intercept`=5`
  2. slope`=1/4`,Y-intercept`=0`
  3. slope`=2`,Y-intercept`=3`

 

4. Find the equation of a line having X-intercept = 3 and Y-intercept = -5

X-intercept : ; Y-intercept :
 

  1. X-intercept`=2`,Y-intercept`=-2`
  2. X-intercept`=-5/3`,Y-intercept`=5`
  3. X-intercept`=-3/5`,Y-intercept`=-3/2`
  4. X-intercept`=3`,Y-intercept`=-5`

7. Find Slope, X-intercept, Y-intercept of a line

1. Find Slope and Y-intercept of a line 7y-4x+9=0

2. Find X-intercept and Y-intercept of a line 7y-4x+9=0

3. Find Slope, X-intercept and Y-intercept of a line 7y-4x+9=0


Line :
     

  1. Line`:2x+3y+4=0`
  2. Line`:3x+6y-8=0`
  3. Line`:4x+5y+7=0`
  4. Line`:3x-2y-12=0`
  5. Line`:7y-4x+9=0`
  6. Line`:5x+2y-11=0`
  7. Line`:3x-y+11=0`
  8. Line`:4x-3y+2=0`

 

4. Find Slope, X-intercept and Y-intercept of the line joining the points `A(3,-5)` and `B(-7,9)`

A ( , ) , B ( , )
 

  1. `A(7,8),B(1,0)`
  2. `A(6,4),B(-1,5)`
  3. `A(2,3),B(7,6)`
  4. `A(-3,4),B(5,-6)`
  5. `A(0,7),B(5,-2)`
  6. `A(0,0),B(-4,-6)`
  7. `A(3,5),B(6,4)`
  8. `A(3,-5),B(-7,9)`

 

8. Find the equation of a line passing through point of intersection of two lines and slope or a point

1. Find the equation of a line passing through point of intersection of lines `2x+3y+4=0` and `3x+6y-8=0` and having slope = 2


Line-1 : , Line-2 : , Slope :
 

  1. Line-1`:x-4y+18=0`,Line-2`:x+y-12=0`,slope`=2`
  2. Line-1`:2x+3y+4=0`,Line-2`:3x+6y-8=0`,slope`=2`
  3. Line-1`:x=3y`,Line-2`:3x=2y+7`,slope`=-1/2`

 

2. Find the equation of a line passing through point of intersection of lines `4x+5y+7=0` and `3x-2y-12=0` and point `A(3,1)`


Line-1 : , Line-2 : , A ( , )
 

  1. Line-1`:x+y+1=0`,Line-2`:3x+y-5=0`,`A(1,-3)`
  2. Line-1`:4x+5y+7=0`,Line-2`:3x-2y-12=0`,`A(3,1)`

9. Find the equation of a line passing through a point and parallel or perpendicular to Line-2

1. Find the equation of a line passing through point `A(5,5)` and parallel to the line `2x+3y+4=0`

2. Find the equation of a line passing through point `A(5,5)` and perpendicular to the line `2x+3y+4=0`


A ( , ) , Line-2 :
   

  1. `A(5,7)`,Line`:2x+3y+5=0`
  2. `A(4,2)`,Line`:3x-2y=5`
  3. `A(5,5)`,Line`:2x+3y+4=0`

 

3. Find the equation of a line passing through point `A(5,5)` and parallel to the line passing `B(1,-2)` and `C(-5,2)`

4. Find the equation of a line passing through point `A(5,5)` and perpendicular to the line passing `B(1,-2)` and `C(-5,2)`


A ( , ) , B ( , ) , C ( , ) ,
   

  1. `A(5,7),B(-1,-1),C(-4,1)`
  2. `A(4,2),B(1,-1),C(3,2)`
  3. `A(5,5),B(1,-2),C(-5,2)`

10. Find the equation of a line passing through point of intersection of Line-1, Line-2 and parallel or perpendicular to Line-3

1. Find the equation of a line passing through point of intersection of the lines `5x+2y-11=0` and `3x-y+11=0` and it is parallel to `4x-3y+2=0`

2. Find the equation of a line passing through point of intersection of the lines `5x+2y-11=0` and `3x-y+11=0` and it is perpendicular to `4x-3y+2=0`


Line-1 : , Line-2 : , Line-3 :
 
   

  1. Line-1`:x-y=1`,Line-2`:2x-3y+1=0`,Line-3`:5x+6y=7`
  2. Line-1`:x-2y+15=0`,Line-2`:3x+y-4=0`,Line-3`:2x-3y+7=0`
  3. Line-1`:5x+2y-11=0`,Line-2`:3x-y+11=0`,Line-3`:4x-3y+2=0`

11. For two lines, find Angle, intersection point and determine if parallel or perpendicular lines

1. Find angle between two lines `5x+2y-11=0` and `3x-y+11=0`

2. Find intersection point of `5x+2y-11=0` and `3x-y+11=0`

3. is parallel lines `2x+3y=11` and `4x+6y=5`

4. is perpendicular lines `2x+3y=11` and `3x-2y=5`


Line-1 : , Line-2 :
       

  1. Line-1`:x-y=1`,Line-2`:2x-3y+1=0`
  2. Line-1`:x-2y+15=0`,Line-2`:3x+y-4=0`
  3. Line-1`:5x+2y-11=0`,Line-2`:3x-y+11=0`

12. Reflection of points about x-axis, y-axis, origin

Find Reflection of pointsA(0,0),B(2,2),C(0,4),D(-2,2) and Reflection about X,Y,O


A ( , ) , B ( , ) , C ( , ) , D ( , ) , Reflection =
 

  1. `A(-2,-2),B(-1,2),C(3,1)` and Reflection about X
  2. `A(2,3),B(7,4),C(8,7),D(3,6)` and Reflection about Y
  3. `A(1,-1),B(-2,2),C(4,8),D(7,5)` and Reflection about O
  4. `A(3,0),B(4,5),C(-1,4),D(-2,-1)` and Reflection about X,Y
  5. `A(3,2),B(5,4),C(3,6),D(1,4)` and Reflection about Y,X
  6. `A(-1,-1),B(1,5),C(2,8)` and Reflection about X
  7. `A(-3,2),B(1,2),C(-3,5)` and Reflection about Y
  8. `A(0,-1),B(3,5),C(5,9)` and Reflection about X
  9. `A(2,8),B(1,5),C(0,2)` and Reflection about Y
  10. `A(0,0),B(2,2),C(0,4),D(-2,2)` and Reflection about X,Y,O

 

Find the equation of the line passing through the points calculator
Find the equation of the line passing through the points calculator
Find the equation of the line passing through the points calculator
Find the equation of the line passing through the points calculator
Find the equation of the line passing through the points calculator
Share this solution or page with your friends.

How do you find the equation of a line that passes through points?

How to Find the Equation of a Line from Two Points.
Find the slope using the slope formula. ... .
Use the slope and one of the points to solve for the y-intercept (b). ... .
Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line..

What is the equation of line passing through two points?

The two-point form of a line is used for finding the equation of a line given two points (x1,y1) ( x 1 , y 1 ) and (x2,y2) ( x 2 , y 2 ) on it. The two point-form of a line is:y−y1=y2−y1x2−x1(x−x1) y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 ) OR y−y2=y2−y1x2−x1(x−x2) y − y 2 = y 2 − y 1 x 2 − x 1 ( x − x 2 ) .

find equation line passing points calculator

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