Home > Geometry calculators > Coordinate Geometry > Find the equation of a line having slope = 2 and Y-intercept = 3 example

6. Find the equation of a line using slope, point, X-intercept, Y-intercept example ( Enter your problem )
  1. Examples
Other related methods
  1. Distance, Slope of two points
  2. Points are Collinear or Triangle or Quadrilateral form
  3. Find Ratio
  4. Find Midpoint or Trisection points or equidistant points on X-Y axis
  5. Find Centroid, Circumcenter, Area of a triangle
  6. Find the equation of a line using slope, point, X-intercept, Y-intercept
  7. Find Slope, X-intercept, Y-intercept of a line
  8. Find the equation of a line passing through point of intersection of two lines and slope or a point
  9. Find the equation of a line passing through a point and parallel or perpendicular to Line-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
  11. Angle between the two lines
  12. Reflection of points about x-axis, y-axis, origin

1. Examples

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

Solution:
The equation of a line with slope m and passing through `(x_1,y_1)` is `y-y_1=m(x-x_1)`

Putting `(5,4)` for `(x_1,y_1)` and `m=1/2,` we get

`:. y-4=1/2(x-5)`

`:. 2(y-4)=(x-5)`

`:. 2y -8=x -5`

`:. x-2y+3=0`



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

Solution:
Here `A(3,5), B(6,4)` are the given points

`:. x_1=3, y_1=5, x_2=6, y_2=4`

The equation of a line AB is
`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

`:. (y-5)/(4-5)=(x-3)/(6-3)`

`:. (y-5)/(-1)=(x-3)/(3)`

`:. 3(y-5)=-(x-3)`

`:. 3y -15=-x +3`

`:. x+3y-18=0`



3. Find the equation of a line having slope `=2` and y intercept `=3`

Solution:
Equation of a line with slope `m` and intercept `c` on Y-axis is `y=mx+c`

Here `m=2` and c=3

`y=2x+3`

`:. 2x-y+3=0`



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

Solution:
Here intercept on X-axis `a=3` and Y-intercept `b=-5`

Equation of a line is
`x/a+y/b=1`

`:. x/(3)+y/(-5)=1`

`:. (x)/(3)-(y)/(5)=1`

`:. 5x-3y=15`



 
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