# Equation of a Line Parallel to a Straight Line

## Trending Questions

**Q.**Draw the graphs of the following equations:

2x − 3y + 6 = 0

2x + 3y − 18 = 0

y − 2 = 0

Find the vertices of the triangle so obtained. Also, find the area of the triangle.

**Q.**Draw the graphs of x − y + 1 = 0 and 3x + 2y − 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and x-axis and shade the triangular area. Calculate the area bounded by these lines and x-axis.

**Q.**Two lines y=3x and x=3y intersects each other at

**Q.**draw the graph of 2x+y-6=0 and 2x-y=-2 also, find the area of the triangle formed by the above lines and x axis

**Q.**Prove that the diagonals of a rectangle ABCD with vertices A(2, −1), B(5, −1), C(5, 6) and D(2, 6) are

equal and bisect each other. [CBSE 2014]

**Q.**

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

2x+3y-2=0

3x+2y-2=0

3x+2y-3=0

3x+2y+3=0

**Q.**

$ABCD$ is a convex quadrilateral. $3,4,5$ and $6$ points are marked on the sides $AB,BC,CD$ and $DA$ respectively. The no. of triangles with vertices on different sides are?

$270$

$220$

$282$

$342$

**Q.**What is value of y so that the line through (3, y) and (2, 7) is parallel to the line passing through (- 1 , 4) and (0, 6)?

- 9
- -8
- 8
- 9

**Q.**29. If A(9, 9), (1, -3) are the end points of hypotenus of a right angled isosceles triangle, then the vertex is. A) (8, -2) B) (-8, 2) C) (8, -8) D) (0, 0)

**Q.**

Find the value of x if the line passing through (x, −3) and (-5, 1) is parallel to the line joining (7, -1) and (0, 3).

-2

3

-3

2

**Q.**

If the slopes of two lines are equal, then the lines are

**Q.**

From the given figure, find :

(i) the co-ordinates of A, B and C.

(ii) the equation of the line through A and parallel to BC.

**Q.**

(i) Find the equation of the line passing through (5, -3) and parallel to x - 3y = 4.

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

**Q.**

(i) Is the line 3x + 4y + 7 = 0 perpendicular to the line 28x - 21y + 50 = 0 ?

(ii) Is the line x - 3y = 4 perpendicular to the line 3x - y = 7 ?

(iii) Is the line 3x + 2y = 5 parallel to the line x + 2y = 1 ?

(iv) Determine x so that the slope of the line through (1, 4) and (x, 2) is 2.

**Q.**

Solve the following system of equations graphically and find the vertices and

area of the triangle formed by these lines and the y-axis.

$4x-y-4=0\phantom{\rule{0ex}{0ex}}3x+2y-14=0$

**Q.**

A line passing through point (12, 94), has y-intercept of 3. Find the x-intercept of the line.

0

1

Not definite

Insufficient data

**Q.**Show graphically that the following given systems of equations is inconsistent i.e. has no solution:

$x-2y=6\phantom{\rule{0ex}{0ex}}3x-6y=0$

**Q.**

The intercepts made by a straight line on the -axis and -axis are –3 and 2 units respectively. Find:

i) the gradient of the line

ii) the equation of the line.

iii) the area of the triangle enclosed between the line and the co-ordinate axes.

2/3, 3y-6=2x, 3 unit

^{2}2/3, 3y-6= x, 5 unit

^{2}3/2, 3y-4=2x, 8unit

^{2}1/3, 2y-6=2x, 3 unit

^{2}

**Q.**

The lines represented by 4x + 3y = 9 and px - 6y + 3 = 0 are parallel. Find the value of p.

**Q.**

Prove that the points (2, 3), (7, 5), (9, 8), (4, 6) are the vertices of a parallelogram.

**Q.**draw the graph of linear equation 3x+y=3, 3x+y=9

**Q.**Find the product of x-intercept and y-intercept of the line 2x+4y=10.

- 12.5

**Q.**In the figure, AB || CD and XY is the transversal.

Which of the following is incorrect?

- p=115∘
- q=115∘
- q=65∘
- r=115∘

**Q.**

Find the value of k, if the line represented by the equation 3x – ky = 12 passes through the point (4, 2). [2 MARKS]

**Q.**

ABCD is a rectangle whose sides AB has equation 3x-12y+5 =0. Find the slopes of the other sides of the rectangle

**Q.**the line segment joining P(-4, 5) and Q(3, 2) intersect the y- axis at R. PM and QN are perpendiculars from P and Q on the x axis.

find: 1) the ratio PR:QR

2) the cordinates of R

3) the area of the quadrilateral PMNQ

**Q.**

If 2y –a2x = 3 and 2y – (4ax +1) = 0 are parallel, find the value of a, where a is a natural number.

**Q.**

Find the equation of the line through the intersection of 2x +y = 8, 3x – 7 = y and parallel to 4x +y = 11.

**Q.**

The perpendicular distance from the origin to a line is 7 and the perpendicular makes an angle of 150∘ with the positive x-axis. Find the equation of the line.

**Q.**The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is