Co-ordinate Geometry — Exercise 21(B)

Draw the graph of :

x = 6

Answer

Draw the graph of :

x + 4 = 0

Answer

Given, equation :

⇒ x + 4 = 0

⇒ x = -4

Draw the graph of :

x - 5 = 0

Answer

Given, equation :

⇒ x - 5 = 0

⇒ x = 5

Draw the graph of :

y = 4

Answer

Draw the graph of :

y + 5 = 0

Answer

Given, equation :

⇒ y + 5 = 0

⇒ y = -5

Draw the graph of :

2y - 7 = 0

Answer

Given,

⇒ 2y - 7 = 0

⇒ 2y = 7

⇒ y = $\dfrac{7}{2}$.

Draw the graph of :

y = x

Answer

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -1, then y = -1

Let x = 0, then y = 0

Let x = 1, then y = 1

Let x = 2, then y = 2

Step 2 :

Make a table for the corresponding values of x and y:

Step 3 :

Plot the points (-1, -1), (0, 0), (1, 1) and (2, 2) on a graph paper and then draw a straight line passing through the points plotted on the graph.

Draw the graph of :

y = -x

Answer

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -1, then y = 1

Let x = 0, then y = 0

Let x = -2, then y = 2

Let x = 2, then y = -2

Step 2 :

Make a table for the corresponding values of x and y:

Step 3 :

Plot the points (-1, 1), (0, 0), (-2, 2) and (2, -2) on a graph paper and then draw a straight line passing through the points plotted on the graph.

Draw the graph of :

y = 2x

Answer

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -1, then y = -2

Let x = 0, then y = 0

Let x = 1, then y = 2

Let x = 2, then y = 4

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (-1, -2), (0, 0), (1, 2) and (2, 4) on a graph paper and then draw a straight line passing through the points plotted on the graph.

Draw the graph of :

y = 3x + 2

Answer

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -1, then y = -1

Let x = 0, then y = 2

Let x = 1, then y = 5

Let x = -2, then y = -4

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (-1, -1), (0, 2), (1, 5) and (-2, -4) on a graph paper and then draw a straight line passing through the points plotted on the graph.

Draw the graph of :

y = 2x - 1

Answer

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 0, then y = -1

Let x = 1, then y = 1

Let x = 2, then y = 3

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (0, -1), (1, 1), (2, 3) on a graph paper and then draw a straight line passing through the points plotted on the graph.

Draw the graph of :

y - x = 5

Answer

Given,

y - x = 5

y = x + 5

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 0, then y = 5

Let x = -5, then y = 0

Let x = -2, then y = 3

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (0, 5), (-5, 0), (-2, 3) on a graph paper and then draw a straight line passing through the points plotted on the graph.

Draw the graph of the equation,

2x + y = 6.

Find the co-ordinates of the points, where the graph meets the co-ordinate axes.

Answer

Given,

2x + y = 6

y = 6 - 2x

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 0, then y = 6

Let x = 1, then y = 4

Let x = 2, then y = 2

Let x = 3, then y = 0

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (0, 6), (1, 4), (2, 2) and (3, 0) on a graph paper and then draw a straight line passing through the points plotted on the graph.

Graph meets x-axis at (3, 0).

Graph meets y-axis at (0, 6).

Draw the graph of the equation,

2x - 3y = 5.

(i) Find the value of y, when x = 4.

(ii) Find the value of x, when y = 3.

Answer

Given,

2x - 3y = 5

3y = 2x - 5

y = $\dfrac{2x - 5}{3}$

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 4, then y = 1

Let x = 2.5, then y = 0

Let x = 1, then y = -1

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (4, 1), (2.5, 0), (1, -1) on a graph paper and then draw a straight line passing through the points plotted on the graph.

(i) To find the value of y, when x = 4 :

Through the point x = 4, draw a vertical straight line which meets the line 2x - 3y = 5 at point C.

Through point C, draw a horizontal line which meets the y-axis at y = 1.

Hence, the value of y = 1, when x = 4.

(ii) To find the value of x, when y = 3 :

Through the point y = 3, draw a horizontal straight line which meets the line 2x - 3y = 5 at point D.

Through point D, draw a vertical line which meets the x-axis at x = 7.

Hence, the value of x = 7, when y = 3.

Solve the simultaneous equations graphically:

y = 2x + 3 and y = 3x + 1

Answer

First Equation : y = 2x + 3

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -1.5, then y = 0

Let x = 0, then y = 3

Let x = 2, then y = 7

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (-1.5, 0), (0, 3), (2, 7) on a graph paper and then draw a straight line passing through the points plotted on the graph.

Second Equation : y = 3x + 1

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 0, then y = 1

Let x = 1, then y = 4

Let x = 2, then y = 7

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (0, 1), (1, 4), (2, 7) on a graph paper and then draw a straight line passing through the points plotted on the graph.

On the same graph paper, draw the graph for each given equation.

Both the straight lines drawn meet at a point. As it is clear from the graph, co-ordinates of the common point are (2, 7).

Hence, x = 2, y = 7.

Solve the simultaneous equations graphically:

x + y = 1 and 3x + 2y = 6

Answer

First Equation : x + y = 1

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 1, then y = 0

Let x = 0, then y = 1

Let x = 4, then y = -3

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (1, 0), (0, 1), (4, -3) on a graph paper and then draw a straight line passing through the points plotted on the graph.

Second Equation : 3x + 2y = 6

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 0, then y = 3

Let x = 2, then y = 0

Let x = 4, then y = -3

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (0, 3), (2, 0), (4, -3) on a graph paper and then draw a straight line passing through the points plotted on the graph.

On the same graph paper, draw the graph for each given equation.

Both the straight lines drawn meet at a point. As it is clear from the graph, co-ordinates of the common point are (4, -3).

Hence, x = 4, y = -3.

Solve the simultaneous equations graphically:

y - 2x = 1 and 5y - x = 14

Answer

First Equation : y - 2x = 1

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -1, then y = -1

Let x = 0, then y = 1

Let x = 1, then y = 3

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (-1, -1), (0, 1), (1, 3) on a graph paper and then draw a straight line passing through the points plotted on the graph.

Second Equation : 5y - x = 14

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 1, then y = 3

Let x = -4, then y = 2

Let x = 6, then y = 4

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (1, 3), (-4, 2), (6, 4) on a graph paper and then draw a straight line passing through the points plotted on the graph.

On the same graph paper, draw the graph for each given equation.

Both the straight lines drawn meet at a point. As it is clear from the graph, co-ordinates of the common point are (1, 3).

Hence, x = 1, y = 3.

Solve the simultaneous equations graphically:

x + 2y = 3 and 4x + 3y = 2

Answer

First Equation : x + 2y = 3

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 1, then y = 1

Let x = 3, then y = 0

Let x = -1, then y = 2

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (1, 1), (3, 0), (-1, 2) on a graph paper and then draw a straight line passing through the points plotted on the graph.

Second Equation : 4x + 3y = 2

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 0.5, then y = 0

Let x = -1, then y = 2

Let x = 2, then y = -2

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (0.5, 0), (-1, 2), (2, -2) on a graph paper and then draw a straight line passing through the points plotted on the graph.

On the same graph paper, draw the graph for each given equation.

Both the straight lines drawn meet at a point. As it is clear from the graph, co-ordinates of the common point are (-1, 2).

Hence, x = -1, y = 2.

Solve the simultaneous equations graphically:

2x + 3y = 2 and x - 2y = 8

Answer

First Equation : 2x + 3y = 2

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 1, then y = 0

Let x = -2, then y = 2

Let x = 4, then y = -2

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (1, 0), (-2, 2), (4, -2) on a graph paper and then draw a straight line passing through the points plotted on the graph.

Second Equation : x - 2y = 8

Step 1 :

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 0, then y = -4

Let x = 8, then y = 0

Let x = 4, then y = -2

Step 2 :

Make a table for the corresponding values of x and y: :

Step 3 :

Plot the points (0, -4), (8, 0), (4, -2) on a graph paper and then draw a straight line passing through the points plotted on the graph.

On the same graph paper, draw the graph for each given equation.

Both the straight lines drawn meet at a point. As it is clear from the graph, co-ordinates of the common point are (4, -2).

Hence, x = 4, y = -2.