Graph of a Linear Function in Two Variables

Q. A bank gives 10% simple interest on deposits made by Senior citizens.
Illustrate by a graph the relation between the deposit and the interest gained. Use the graph to compute
(i) The annual interest obtained for an investment of ₹450.
(ii) The amount a Senior citizen has to invest to get an annual simple interest of ₹80.

1. ₹40 and ₹800
2. ₹45 and ₹750
3. ₹40 and ₹400
4. ₹45 and ₹800

Q. Draw the graph of y = x + 10.
Find the coordinates of the point of interserction with the axes.(Take 1 cm = 10 units.)

1. (10, 0) and (0, -10)
2. (-10, 10) and (0, 10)
3. (-10, 0) and (0, 10)
4. (10, 0) and (0, 10)

Q. Find the equation of the perpendicular from the point(3, -1, 11)to the line x/2=y-2/3=z-3/4 also find the coordinates of foots of the perpendicular and length of the perpendicular?

Q. If $b=$ in the equation $ax+by+c=0$ where $a,b$ and $c$ are constants, then the line represented by the equation is parallel to Y-axis.

1. 1
2. 2
3. \N

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.

What we need for fixing the point on the graph paper ?

Q.

At which point does 4x + 5y = 10 cut the y axis?

1. (0, 2)

2. (2, 0)

3. (-2, 0)

4. (0, -2)

Q. Find graphically the coordinates of the vertices of a triangle whose sides have 3 equations; x 2y = 4, x = 4 & x y = 3.

Q.

Find the point on Cartesian plane where the line 5x - y = 10 intersect the x - axis.

1. x = 2, y = 5

2. x = 0, y = 2

3. x = 2, y = 0

4. x = 0, y = 0

Q.

Using graph, find the quantity when cost is Rs 8.

1. 5 units

2. 4 units

3. 3 units

4. 6 units

Q.

A linear equation in two variables can be written in the form $ax+by+c=0$. Now look at the linear equations in Column-I and match them with their constant term$c$ written in the Column-II.

Column-I		Column -II
(a)	$5x+7y=-27$	(p)	$-17$
(b)	$2x+y=17$	(q)	$17$
(c)	$3y-5x+17=0$	(r)	$-27$
(d)	$4x-3y-27=0$	(s)	$27$

1. (a)⇢ r; (b)⇢ p; (c)⇢ q; (d)⇢ s

2. (a)⇢ s; (b)⇢ p; (c)⇢ q; (d)⇢ r

3. (a)⇢ s; (b)⇢ q; (c)⇢ p; (d)⇢ r

4. (a)⇢ r; (b)⇢ q; (c)⇢ p; (d)⇢ s

Q.

Using graph, find the cost when quantity is 3 units.

1. Rs 5

2. Rs 6

3. Rs 8

4. Rs 4

Q. If the line represented by the equation $3x+4y+c=0$ passes through the origin, then $c$ =.

1. $2$
2. $1$
3. $0$

Q. The equation of a circle with radius 5 and touching both the coordinate axes is
(a) x² + y² ± 10x ± 10y + 5 = 0
(b) x² + y² ± 10x ± 10y = 0
(c) x² + y² ± 10x ± 10y + 25 = 0
(d) x² + y² ± 10x ± 10y + 51 = 0

Q.

Mayank deposited Rs. 1400 in a bank at the rate of 10% per annum. Draw a linear graph which shows the relationship between time and the interest earned by Mayank. [4 MARKS]

Q.

Using graph, find the cost when quantity is 7 units.

1. Rs 13

2. Rs 16

3. Rs 14

4. Rs 15

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. ₹750
4. ₹800

Q.

I plot the side of a square on one axis and the area of square on another axis. Draw the graph. Is the graph linear? [2 MARKS]

Q. equation of a parabola whose vertex is (2, -3)axis is parallel to the x axis and latusrectum 8 is

Q. If a point $(1,2)$ lies on the line represented by the equation $3y=ax+7,$ then the value of $a$ is .

1. $-1$

2. $1$
3. $2$

Q. The value of $b$ in $5x+9y+1=0$ is 9, where $ax+by+c=0$ is the general form of a linear equation in two variables.

1. False
2. True

Q. $(0,1)$ is a point on the line represented by the equation
$y=x+1.$

1. False
2. True

Q. The co-ordinate is the perpendicular distance of the point from the x-axis.

1. x
2. y
3. z

Q. Which of the following equations pass through origin?

1. 2x+3y+6=0
2. 5x+3y=0
3. 9x+5y+8=0
4. 7x+2y=0
5. x+y=6
6. 4y+1y+0=0
7. 6x+4y-8= -8
8. 9x+5y+0x=0