Equation of a Line with Respect to Another

Q. Solve the following system of linear equations graphically :

3x + y − 11 = 0, x − y − 1 = 0.
Shade the region bounded by these lines and y-axis. Also, find the area of the region bounded by the these lines and y-axis.

Q. Solve graphically the system of linear equations:

4x − 3y + 4 = 0
4x + 3y − 20 = 0

Find the area bounded by these lines and x-axis.

Q.

Write four solutions for the given equation:

$\frac{2}{3}x-y=4$

Q. Solve the following system of equations graphically.

2x − 3y + 6 = 0
2x + 3y − 18 = 0

Also, find the area of the region bounded by these two lines and y-axis.

Q. If A(-1, 8), B(4, -2) and C(-5, -3) are the vertices of a triangle, then find the equation of the median through (-1, 8).

Q.

If the line $(3x+14y+7)+k(5x+7y+6)=0$ is parallel to the y-axis, then the value of $k$ is

1. $\frac{1}{3}$

2. $\frac{-3}{5}$

3. $-2$

4. $2$

Q.

Find the equation of the line passing through the point (3, 2) and parallel to the line $4x+y=11$.

1. $3x+4y-14=0$

2. $4x+y=14$

3. $x+4y-10=0$

4. $3x+y-11=0$

Q. Find the equation of the straight line that has y - intercept 5 and is parallel to the straight line x - 3y = 3

1. 2x - 3y +12 = 0

2. 3x - y + 5 = 0

3. x - y +5=0

4. x - 3y + 15 =0

Q.

The equation of a line having a slope of 2 and y-intercept of 6 units is ______.

1. y = 2x + 6

2. y = 2x - 6

3. y = -2x + 6

4. y = 6x + 2

Q. Point A = (3, 5) , P = (1, 3), and Q = (2, 5).
If line AB is parallel to line PQ, find the equation of line AB.

Q. 5x – 2y = 3

Q.

Find the equation of the line parallel to the line $3x+2y=8$ and passing through the point $(0,1)$.

1. 2x+3y-2=0

2. 3x+2y-2=0

3. 3x+2y-3=0

4. 3x+2y+3=0

Q.

A(-1, 8), B(4, -2) and C(-5, -3) are the vertices of a triangle, find the equation of the median through (-1, 8).

1. 21x + y + 13 = 0

2. 2x + y - 6 = 0

3. 11x - 4y + 43 = 0

4. x - 9y - 22 = 0

Q. The point (-3, 1) lies on which of the following equations?

1. 2x - y + 3=0
2. 3x + 6y = 0
3. x - 2y - 4=0
4. x + 2y + 1=0

Q. Given equation is $5x=4y+7$, then the slope is $\frac{5}{m}$ find the value of m.

Q.

Through the point (3, 4) are drawn to straight line each inclined at 45 degree to the straight line x-y=2. Find their equations and also find the areas of triangle bounded by the three lines