Graphical Representation of a Linear Equation in Two Variables

Q. Draw the graph of the linear equation 3x + 4y = 6. At what points, does the graph cut the x-axis and the y-axis?

Q. The distance between line $y=3$ and $y=-3$ is ___ units.

1. 0
2. 3
3. 6
4. 9

Q.

The line x + y = 3 lies closer to the origin as compared to the line x + y = 5 when plotted on the cartesian plane.

1. False

2. True

Q.

A linear equation in two variables has only 1 solution.

1. True

2. False

Q. The equation of the graph given below is .

1. y = 2x - 4
2. 3y = 6x - 15
3. y - 2x = 4
4. y = 2x + 2

Q. Draw a graph of the line $x-2y=3$. From the graph, find the coordinates of the point when
i) $x=-5$
ii) $y=0$

Q. If the graph (O is the origin) of the equation $4x+3y=12$ cuts the coordinate axes at A and B respectively, then the length of the hypotenuse of right angle triangle AOB is :

1. 3 units
2. 5 units
3. 2 units
4. 4 units

Q.

The graph of the linear equation: 2x+3y=6, cuts the y-axis at the point:

1. (2, 0)

2. (3, 0)

3. (0, 2)

4. (0, 3)

Q. axes are required to plot a linear equation in two variables.

1. 2
2. 3
3. 4

Q. Question 7
Write whether the following statement is True or False?
The graph of every linear equation in two variables need not be a line.

Q. Question 6
Write whether the following statement is True or False?​​​​​​​
Every point on the graph of a linear equation in two variables does not represent a solution of the linear equation.

Q. If the point (5, 4) lies on the graph of the equation 7y = ax+8, find the value of a. [3 MARKS]

Q.

A linear equation in two variables has only 1 solution.

1. True

2. False

Q. Plot the point $P(2,-6)$ on a graph paper and from it draw $PM$ and $PN$ perpendiculars to $x-axis$ and $y-axis$, respectively. Write the coordinates of the points $M$ and $N$.

Q. Which of the following line(s) would make a right-angled triangle with the coordinate axes?

1. $3x+2y=6$
2. $3x+2y=-6$
3. $x-y=1$
4. $3y=15$

Q. If the point (5, 4) lies on the graph of the equation 7y = ax + 8, find the value of a.

Q.

What will be the linear equation for the given graph?

1. x=2y

2. y=2x+5

3. y=2x+3

4. 2y=x+1

Q. The equation of the graph given below is .

1. y = 2x - 4
2. 3y = 6x - 15
3. y - 2x = 4
4. y = 2x + 2

Q. The points where abscissa is $5$ are $B=(5,0),H=(5,5)$and $G=(5,-3)$.
If true, then enter $1$ and if false, then enter $0$.

Q. Use graph paper for this question. The point $(5,3)$ was reflected in the origin to get the image $P^{\prime }$.
1. write down the coordinates of $p^{\prime }$.
2. If M is foot of perpendicular from $p$ to x-axis, find the coordinates of $M$.
3. If $N$ id the foot of perpendicular from $p^{\prime }$ to the x-axis, find the coordinates of $N$.
4. Name the figure $PM{P}^{\prime }N$.
5. Find the area of the area $PM{P}^{\prime }N$.

Q.

equation x=7 in two variables can be written as _______________ .

Q. Write whether the following statements are True or False?
(i) The point (0, 3) lies on the graph of the linear equation 3x + 4y = 12.
(ii) The graph of the linear equation x + 2y = 7 passes through the point (0, 7).

Q. The ordinate is half of the abscissa, then the point $E=(6,3)$.
If true, then enter $1$ and if false, then enter $0$.

Q. Write whether the following statements are True or False?
(i) The point (0, 3) lies on the graph of the linear equation 3x + 4y = 12.
(ii) The graph of the linear equation x + 2y = 7 passes through the point (0, 7).

Q. $x-5=0$ is parallel to $y-$axis. Find the value of $x$ co-ordinate where it crosses $x-axis$.

Q.

The graph of the linear equation: 2x+3y=6, cuts the y-axis at the point:

1. (2, 0)

2. (3, 0)

3. (0, 2)

4. (0, 3)