Equation of line passing through a given point and parallel to the line passing given points calculator

SolutionMethods

1. Find the equation of the line passing through the point

$A(1,3)$ and parallel to line passing through the points

$B(3,-5)$ and

$C(-6,1)$

2. Find the equation of the line passing through the point

$A(4,-5)$ and parallel to line passing through the points

$B(3,7)$ and

$C(-2,4)$

3. Find the equation of the line passing through the point

$A(-1,3)$ and parallel to line passing through the points

$B(0,2)$ and

$C(4,5)$

4. Find the equation of the line passing through the point

$A(2,-3)$ and parallel to line passing through the points

$B(1,2)$ and

$C(-1,5)$

5. Find the equation of the line passing through the point

$A(4,2)$ and parallel to line passing through the points

$B(1,-1)$ and

$C(3,2)$

6. Find the equation of the line passing through the point

$A(5,5)$ and parallel to line passing through the points

$B(1,-2)$ and

$C(-5,2)$

Example

1. Find the equation of the line passing through the point $A(1,3)$ and parallel to line passing through the points $B(3,-5)$ and $C(-6,1)$

Solution:
Given points are

$A(1,3)$ ,

$B(3,-5)$ and

$C(-6,1)$

When two lines are parallel, their slopes are equal.

We shall first find the slope of

$B(3,-5)$ and

$C(-6,1)$

Points are

$B(3,-5),C(-6,1)$

$:. x_1=3,y_1=-5,x_2=-6,y_2=1$

Slope of the line,

$m=(y_2-y_1)/(x_2-x_1)$

$:. m=(1+5)/(-6-3)$

$:. m=(6)/(-9)$

$:. m=-2/3$

$:.$ Slope

$=-2/3$

Hence, slope of the line parallel to this line is also

$-2/3$

$(:' m_1=m_2)$

The equation of a line with slope m and passing through

$(x_1,y_1)$ is

$y-y_1=m(x-x_1)$

Here Point

$(x_1,y_1)=(1,3)$ and Slope

$m=-2/3$ (given)

$:. y-3=-2/3(x-1)$

$:. 3(y-3)=-2(x-1)$

$:. 3y -9=-2x +2$

$:. 2x+3y-11=0$

Hence, The equation of line is

$2x+3y-11=0$

2. Find the equation of the line passing through the point $A(4,-5)$ and parallel to line passing through the points $B(3,7)$ and $C(-2,4)$

Solution:
Given points are

$A(4,-5)$ ,

$B(3,7)$ and

$C(-2,4)$

When two lines are parallel, their slopes are equal.

We shall first find the slope of

$B(3,7)$ and

$C(-2,4)$

Points are

$B(3,7),C(-2,4)$

$:. x_1=3,y_1=7,x_2=-2,y_2=4$

Slope of the line,

$m=(y_2-y_1)/(x_2-x_1)$

$:. m=(4-7)/(-2-3)$

$:. m=(-3)/(-5)$

$:. m=3/5$

$:.$ Slope

$=3/5$

Hence, slope of the line parallel to this line is also

$3/5$

$(:' m_1=m_2)$

The equation of a line with slope m and passing through

$(x_1,y_1)$ is

$y-y_1=m(x-x_1)$

Here Point

$(x_1,y_1)=(4,-5)$ and Slope

$m=3/5$ (given)

$:. y+5=3/5(x-4)$

$:. 5(y+5)=3(x-4)$

$:. 5y +25=3x -12$

$:. 3x-5y-37=0$

Hence, The equation of line is

$3x-5y-37=0$

3. Find the equation of the line passing through the point $A(-1,3)$ and parallel to line passing through the points $B(0,2)$ and $C(4,5)$

Solution:
Given points are

$A(-1,3)$ ,

$B(0,2)$ and

$C(4,5)$

When two lines are parallel, their slopes are equal.

We shall first find the slope of

$B(0,2)$ and

$C(4,5)$

Points are

$B(0,2),C(4,5)$

$:. x_1=0,y_1=2,x_2=4,y_2=5$

Slope of the line,

$m=(y_2-y_1)/(x_2-x_1)$

$:. m=(5-2)/(4-0)$

$:. m=(3)/(4)$

$:.$ Slope

$=3/4$

Hence, slope of the line parallel to this line is also

$3/4$

$(:' m_1=m_2)$

The equation of a line with slope m and passing through

$(x_1,y_1)$ is

$y-y_1=m(x-x_1)$

Here Point

$(x_1,y_1)=(-1,3)$ and Slope

$m=3/4$ (given)

$:. y-3=3/4(x+1)$

$:. 4(y-3)=3(x+1)$

$:. 4y -12=3x +3$

$:. 3x-4y+15=0$

Hence, The equation of line is

$3x-4y+15=0$

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

Solution:
Given points are

$A(2,-3)$ ,

$B(1,2)$ and

$C(-1,5)$

When two lines are parallel, their slopes are equal.

We shall first find the slope of

$B(1,2)$ and

$C(-1,5)$

Points are

$B(1,2),C(-1,5)$

$:. x_1=1,y_1=2,x_2=-1,y_2=5$

Slope of the line,

$m=(y_2-y_1)/(x_2-x_1)$

$:. m=(5-2)/(-1-1)$

$:. m=(3)/(-2)$

$:. m=-3/2$

$:.$ Slope

$=-3/2$

Hence, slope of the line parallel to this line is also

$-3/2$

$(:' m_1=m_2)$

The equation of a line with slope m and passing through

$(x_1,y_1)$ is

$y-y_1=m(x-x_1)$

Here Point

$(x_1,y_1)=(2,-3)$ and Slope

$m=-3/2$ (given)

$:. y+3=-3/2(x-2)$

$:. 2(y+3)=-3(x-2)$

$:. 2y +6=-3x +6$

$:. 3x+2y=0$

Hence, The equation of line is

$3x+2y=0$

5. Find the equation of the line passing through the point $A(4,2)$ and parallel to line passing through the points $B(1,-1)$ and $C(3,2)$

Solution:
Given points are

$A(4,2)$ ,

$B(1,-1)$ and

$C(3,2)$

When two lines are parallel, their slopes are equal.

We shall first find the slope of

$B(1,-1)$ and

$C(3,2)$

Points are

$B(1,-1),C(3,2)$

$:. x_1=1,y_1=-1,x_2=3,y_2=2$

Slope of the line,

$m=(y_2-y_1)/(x_2-x_1)$

$:. m=(2+1)/(3-1)$

$:. m=(3)/(2)$

$:.$ Slope

$=3/2$

Hence, slope of the line parallel to this line is also

$3/2$

$(:' m_1=m_2)$

The equation of a line with slope m and passing through

$(x_1,y_1)$ is

$y-y_1=m(x-x_1)$

Here Point

$(x_1,y_1)=(4,2)$ and Slope

$m=3/2$ (given)

$:. y-2=3/2(x-4)$

$:. 2(y-2)=3(x-4)$

$:. 2y -4=3x -12$

$:. 3x-2y-8=0$

Hence, The equation of line is

$3x-2y-8=0$

6. Find the equation of the line passing through the point $A(5,5)$ and parallel to line passing through the points $B(1,-2)$ and $C(-5,2)$

Solution:
Given points are

$A(5,5)$ ,

$B(1,-2)$ and

$C(-5,2)$

When two lines are parallel, their slopes are equal.

We shall first find the slope of

$B(1,-2)$ and

$C(-5,2)$

Points are

$B(1,-2),C(-5,2)$

$:. x_1=1,y_1=-2,x_2=-5,y_2=2$

Slope of the line,

$m=(y_2-y_1)/(x_2-x_1)$

$:. m=(2+2)/(-5-1)$

$:. m=(4)/(-6)$

$:. m=-2/3$

$:.$ Slope

$=-2/3$

Hence, slope of the line parallel to this line is also

$-2/3$

$(:' m_1=m_2)$

The equation of a line with slope m and passing through

$(x_1,y_1)$ is

$y-y_1=m(x-x_1)$

Here Point

$(x_1,y_1)=(5,5)$ and Slope

$m=-2/3$ (given)

$:. y-5=-2/3(x-5)$

$:. 3(y-5)=-2(x-5)$

$:. 3y -15=-2x +10$

$:. 2x+3y-25=0$

Hence, The equation of line is

$2x+3y-25=0$