##### Class 9^{th} Mathematics AP Board Solution

**Exercise 6.3**

- 2y = -x + 1 Draw the graph of each of the following linear equations.…
- -x + y = 6 Draw the graph of each of the following linear equations.…
- 3x + 5y = 15 Draw the graph of each of the following linear equations.…
- x/2 - y/3 = 3 Draw the graph of each of the following linear equations.…
- y = x Draw the graph of each of the following linear equations.
- y = 2x Draw the graph of each of the following linear equations.
- y = -2x Draw the graph of each of the following linear equations.…
- y = 3x Draw the graph of each of the following linear equations.
- y = -3x Draw the graph of each of the following linear equations.…
- Answer the following question related to above graphs. i) Are all these…
- Draw the graph of the equation 2x + 3y = 11. Find from the graph value of y when…
- Draw the graph of the equation y - x = 2. Find from the graph i) the value of y…
- Draw the graph of the equation 2x + 3y = 12. Find the solutions from the graph…
- 6x - 3y = 12 Draw the graph of each of the equations given below and also find…
- - x + 4y = 8 Draw the graph of each of the equations given below and also find…
- 3x + 2y + 6 = 0 Draw the graph of each of the equations given below and also…
- Rajiya and Preethi two students of Class IX together collected ₹ 1000 for the…
- Gopaiah sowed wheat and paddy in two fields of total area 5000 square meters.…
- The force applied on a body of mass 6 kg. is directly proportional to the…
- A stone is falling from a mountain. The velocity of the stone is given by V =…
- In a election 60% of voters cast their votes. Form an equation and draw the…
- When Rupa was born, his father was 25 years old. Form an equation and draw a…
- An auto charges ₹ 15 for first kilometer and ₹ 8 each for each subsequent…
- A lending library has fixed charge for the first three days and an additional…
- The parking charges of a car in Hyderabad Railway station for first two hours…
- Sameera was driving a car with uniform speed of 60 kmph. Draw distance-time…
- The ratio of molecular weight of Hydrogen and Oxygen in water is 1:8. Set up an…
- In a mixture of 28 litres, the ratio of milk and water is 5:2. Set up the…
- In countries like USA and Canada temperature is measured in Fahrenheit where as…

**Exercise 6.4**

- a) On the number line and b) On the Cartesian plane x = 3 Give the graphical…
- a) On the number line and b) On the Cartesian plane y + 3 = 0 Give the…
- a) On the number line and b) On the Cartesian plane y = 4 Give the graphical…
- a) On the number line and b) On the Cartesian plane 2x - 9 = 0 Give the…
- a) On the number line and b) On the Cartesian plane 3x + 5 = 0 Give the…
- Give the graphical representation of 2x - 11 = 0 as an equation in i) one…
- Solve the equation 3x + 2 = 8x - 8 and represent the solution on i) the number…
- Write the equation of the line parallel to X-axis, and passing through the point…
- Write the equation of the line parallel to Y-axis and passing through the point…
- Write the equation of three lines that are (i) parallel to the X-axis (ii)…

###### Exercise 6.3

**Question 1.**

Draw the graph of each of the following linear equations.

2y = -x + 1

**Answer:**

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH:

**Question 2.**

Draw the graph of each of the following linear equations.

–x + y = 6

**Answer:**

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH:

**Question 3.**

Draw the graph of each of the following linear equations.

3x + 5y = 15

**Answer:**

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH:

**Question 4.**

**Answer:**

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH:

**Question 5.**

Draw the graph of each of the following linear equations.

y = x

**Answer:**

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH:

**Question 6.**

Draw the graph of each of the following linear equations.

y = 2x

**Answer:**

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH:

**Question 7.**

Draw the graph of each of the following linear equations.

y = -2x

**Answer:**

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH:

**Question 8.**

Draw the graph of each of the following linear equations.

y = 3x

**Answer:**

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH:

**Question 9.**

Draw the graph of each of the following linear equations.

y = -3x

**Answer:**

(Note: ∵ equation is linear graph will always be straight line.) Table of solutions for the given equation-

GRAPH:

**Question 10.**

Answer the following question related to above graphs.

i) Are all these equations of the form y = mx, where m is a real number?

ii) Are all these graphs passing through the origin?

iii) What can you conclude about these graphs?

**Answer:**

(i) Yes, all these are equations of the form y = mx, where m is a real number and m = 1,2,-2,3,-3 respectively in the above equations.

(ii) Yes, all these are graphs passing through the origin, i.e., pt. A in every graph

(iii) ∴ we can conclude that every graph of type y = mx passes through origin, where m is a real number.

**Question 11.**

Draw the graph of the equation 2x + 3y = 11. Find from the graph value of y when x = 1

**Answer:**

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH:

From the graph (pt. E) we can see that for x = 1, the y = 3.

(Note: Also we can put x = 1 in the given equation and can find the value of y-

We have,

At x = 1,

⇒ y = 3

**Question 12.**

Draw the graph of the equation y - x = 2. Find from the graph

i) the value of y when x = 4

ii) the value of x when y = -3

**Answer:**

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH:

i)the value of y when x = 4 is y = 6 (pt. E)

ii) the value of x when y = -3 is y = -5 (pt. F)

**Question 13.**

Draw the graph of the equation 2x + 3y = 12. Find the solutions from the graph

i) Whose y-coordinate is 3

ii) Whose x-coordinate is -3

**Answer:**

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH:

(i) From the graph, we can see that for y = 3 is pt. E and the

(ii) From the graph, we can see that for x = -3 is pt. F and the corresponding y = 6 for that.

**Question 14.**

Draw the graph of each of the equations given below and also find the coordinates of the points where the graph cuts the coordinate axes

6x - 3y = 12

**Answer:**

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH:

⇒ ∴ the pts. Where graph cuts the co-ordinate axis(i.e., where x = 0 and where y = 0) are pt. A = (2,0) and pt. B = (0,-4)

**Question 15.**

Draw the graph of each of the equations given below and also find the coordinates of the points where the graph cuts the coordinate axes

- x + 4y = 8

**Answer:**

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

⇒ ∴ the pts. Where graph cuts the co-ordinate axis(i.e., where x = 0 and where y = 0) are pt. A = (-8,0) and pt. B = (0,2).

**Question 16.**

Draw the graph of each of the equations given below and also find the coordinates of the points where the graph cuts the coordinate axes

3x + 2y + 6 = 0

**Answer:**

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH:

⇒ ∴ the pts. Where graph cuts the co-ordinate axis(i.e., where x = 0 and where y = 0) are pt. A = (-2,0) and pt. B = (0,-3).

**Question 17.**

Rajiya and Preethi two students of Class IX together collected ₹ 1000 for the Prime Minister Relief Fund for victims of natural calamities. Write a linear equation and draw a graph to depict the statement.

**Answer:**

Given that together Rajiya and Preethi collected Rs.1000.

Now, Let the amount collected by Rajiya be Rs. x and by Preethi be Rs. y.

∴ the linear equation will be-

⇒ x + y = 1000

(Note: ∵ equation is linear graph will always be straight line.)

Table of solutions for the given equation-

GRAPH: