Solutions of Linear Equation in 2 Variables on a Graph

Q. Question 6
The given figure shows the distance-time graph of three objects A, B and C. Study the graph and answer the following questions:

(a) Which of the three is travelling the fastest?
(b) Are all three ever at the same point on the road?
(c) How far has C travelled when B passes A?
(d) How far has B travelled by the time it passes C?

Q.

Draw the graphs of the lines x - y = 1 and 2x + y = 8. Shade the area formed by these two lines and the y - axis. Also, find this area.

Q.

Draw the graph of the equation 2x + 3y = 12. From the graph, find the coordinates of the point:

(i) whose y-coordinates is 3. (ii) whose x-coordinate is - 3.

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 y-axis. Also, find the area of the triangle.

Q.

Draw the graph of the equation 2x + y = 6. Shade the region bounded by the graph and the coordinate axes. Also, find the area of the shaded region.

Q. Draw the graphs of the lines 2x + y = 6 and 2x - y + 2 = 0. Shade the region bounded by these lines and the x - axis. Find the area of the shaded region.

Q. Draw the graph of two lines, whose equations are 3x − 2y + 6 = 0 and x + 2y − 6 = 0 on the same graph paper. Find the area of triangle formed by the two lines and x-axis.

Q.

Draw the graph for each of 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 $\frac{x}{3}+\frac{y}{4}=1.$ Also, find the area of the triangle formed by the line and the coordinates axes.

Q.

Aarushi was driving a car with uniform speed of 60 km/h. Draw distance-time graph. From the graph, find the distance travelled by Aarushi in

(i) $2\frac{1}{2}Hours$ (ii) $\frac{1}{2}Hour$

Q. Draw the graphs of the linear equations 4x − 3y + 4 = 0 and 4x + 3y −20 = 0. Find the area bounded by these lines and x-axis.

Q.

Which of the following graphs will always pass through origin?

1. y = x

2. x = 2y + 4

3. x = 1

4. y = x + 3

Q.

Solutions of the equation 2x + 5y = 0 is:

1. -3, 2

2. 0, 0

3. 0, 4

4. 3, 0

Q.

Point A $\left(4,1\right)$ lies on a line:

1. $x+2y=5$

2. $x+2y=6$

3. $x+2y=16$

4. $x+2y=-6$

Q. The graph of equation 5x-3y=10 cuts the x axis at the point:
A (0, -10/3)
B (-2, 0)
C (2, 0)
D (0, 0)

Q.

The graph of the linear equation 3x - 2y = 6 cuts the y-axis at the point (0, 3).

1. True

2. False

Q.

Draw the graphs of the lines 2x + y = 6 and 2x - y + 2 = 0. Shade the region bounded by these lines and the x - axis. Find the area of the shaded region.

Q.

The point lying on the equation 2x - y = 5 is:

1. (-3, 1)

2. (6, 1)

3. (3, 4)

4. (2, -1)

Q. If the points (0, 1) and (1, 0) lie on the graph of the equation y=mx+c, then find the values of m and c.

Q.

Find the point at which the line represented by the equation $6x+5y=9,$ intersects the x-axis.

1. $(1,0)$

2. $(0,\frac{3}{2})$

3. $(\frac{3}{2},0)$

4. $(2,3)$

Q. Question 19
The point of the term (a, -a) always lies on the line:

A) x = a
B) y = -a
C) y = x​​​​​​​
D) x + y = 0​​​​​​​

Q. The graph of the line y = 2 passes through the point
(a) (2, 0)
(b) (2, 3)
(c) (5, 2)
(d) None of these

Q. The following tables gives the quantity of rice and its cost.

Quantity of rice (in kg)	4	6	8	10
Cost of rice in ₹	200	300	400	500

Plot the graph of quantity of rice and its cost and find the cost for 14 kg of rice.

1. ₹700
2. ₹600
3. ₹800
4. ₹750

Q. The value of 'p', for which the point (p, 2) lies on the line 3x + y = 11 is ____.

1. 2
2. 3
3. 9
4. 1

Q. Find the value of a & b if the line 6bx + at = 24 passes through point (2, 0)& (0, 2)

Q.

The x and y intercepts of the line 2y = 3x

1. 

2. 

3. 

4. 

Q. The linear equation $5x+12y=48$ cuts the x-axis at

1. $(0,4)$
2. $(4,0)$
3. $(0,\frac{48}{5})$
4. $(\frac{48}{5},0)$

Q.

Give the geometric representations of 2x + 9 = 0 as an equation

(1) in one variable

(2) in two variables

Q.

In the given graph, the sum of the x co-ordinate and y co-ordinate of the point is _____ .

1. 2

2. 3
3. 4
4. 5

Q.

A point on the line x + y = 0 can be represented as (a, -a).

1. True

2. False