Equations Representing Parallel lines

Q. The path of a train A is given by the equation 3x + 4y − 12 = 0 and the path of another train B is given by the equation 6x + 8y − 48 = 0. Represent this situation graphically.

Q. Y-intercept of a line can not be negative.

1. True
2. False

Q. Draw the graphs of the following linear equations on the same graph paper:
2x + 3y = 12, x − y = 1

Find the coordinates of the vertices of the triangle formed by the two straight lines and the area bounded by these lines and x-axis.

Q.

Find the equation of a line parallel to the y-axis passing through the point P(4, -1).

1. y = -1

2. y = 4

3. x = -1

4. x = 4

Q.

at what points does the graph of the linear equation x+y=5 meet a line which is parallel to the y axis , at a distance 2 units from the origin and in positive direction of x axis.

Q.

The equation of the line shown in the figure is.

1. x = 1

2. y = 1

3. y = 0

4. x = 0

Q. The equation of line m is .

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

Q. The equation of line parallel to y-axis is:

(a) x = 1
(b) x + y = 0
(c) y = 0
(d) y = 1

Q.

The graph of the equation of the form y=mx is a line which always passes through:

1. (0, y)

2. (x, 0)

3. (0, m)

4. (0, 0)

Q. Draw the graph of each of the equations given below. Also, find the coordinates of the points where the graph cuts the coordinate axes:

(i) 6x − 3y = 12

(ii) −x + 4y = 8

(iii) 2x + y = 6

(iv) 3x + 2y + 6 = 0

Q. Find the equation of a line parallel to the y-axis passing through the point P(4, -1).

Q. Find the equation of a line parallel to the y-axis passing through the point P(4, -1).

Q. Draw the graph of the equation y = 3x. From your graph, find the value of y when x = −2.

Q.

The graph given is represented by which of the following equations?

1. y = x - 1

2. x - 2y = 1

3. y = x

4. y = 2x + 1

Q. y − 4 = 0 is the equation of a line
(a) parallel to the x-axis and passing through (4, 0)
(b) parallel to the x-axis and passing through (0, 4)
(c) parallel to the y-axis and passing through (0, 4)
(d) None of these

Q. Fill in the blanks.
(i) For the line 4x + 3y = 12, x-intercept = ...... and y-intercept = ......
(ii) If x = 4, y = 3 is a solution of 2x + ky = 14, then k = ......
(iii) If the point P(p, 4) lies on the line 3x + y = 10, then p = ......

Q. Draw the graphs for the equations x + y = 6 and x − y = 2 on the same graph paper and find the coordinates of the point where the two straight lines intersect.

Q. Draw the graph of the equation x + 2y − 3 = 0. From your graph, find the value of y when x = 5.

Q. Line AB is parallel to Y-axis at a distance of 3 units to the left of it. Line PQ is parallel to X-axis at a distance of 4 units above it. Write the equations of the lines, draw the graphs and also write the point intersection of these two lines.

Q. The graph of the linear equation 2x + 5y = 10 is the line which meets the y-axis at the point
(a) (0, 2)
(b) (5, 0)
(c) $\left(\frac{1}{2},2\right)$
(d) (2, 1.2)

Q.

------------------- is the equation of y-axis.

1. x = 0

2. y = 1

3. y = -1

4. y = 0

Q. Lines x – y = 0, x + y = 0 and X-axis are concurrent at:

1. A point in X-axis
2. A point on Y-axis
3. Origin
4. Quadrant I

Q. Do the point $\mathrm{P}\left(\frac{3}{2},5\right)$ lie on the line x + y$=\frac{13}{2}$? If so, draw the graph and check it.

Q. Line CD is parallel to Y-axis and passing through the point A(−4, 3). Write the equation of line CD.

Q.

A line has equation x + y = 0

So the line must

1. Be parallel to y - axis

2. Be parallel to y - axis

3. Must pass through (1, 1)

4. Pass through the origin

Q. Write the equation of the line that is parallel to x-axis and passing through the point (2, -5). $\left[1\text{Mark}\right]$

Q. $\sqrt{3}x-y=2$ and $\sqrt{6}x-\sqrt{2}y=2$ are lines.

1. coincident
2. parallel
3. intersecting

Q. Parallel lines have .

1. one solution
2. no solution
3. 4 solutions

Q. Draw the graph of the equation 2x + y = 6. Find the coordinates of the point, where the graph cuts the x-axis.

Q. Does the point M (2, 4) lie on the graph of x + y = 6? Verify your answer by drawing the graph.