Given the inequality equality is:

⇒ 2a + 3b ≤ 10;

First we change this inequality equation by equality so that we can find coordinates for graph.

On changing this equation by equality then the equation becomes:

So we can write the equation as:

⇒ 2a + 3b ≤ 10;

⇒ 2a + 3b = 10;

Now we find the value of one coordinate, here in the equation we can find coordinates of b;

⇒ 2a + 3b = 10;

⇒ 3b = -2a + 10;

On further solving we get the value of b is:

⇒ b = -2a + 10;

3

For further solving we put different values of “a” so that we can find the “b” coordinates for plotting the graph.

If we put the value of a is -3 then we get:

Put a = -3;

⇒ b = -2a + 10;

3

⇒ b = -2(-3) + 10;

3

⇒ b = 6 + 10;

3

On further solving we get:

⇒ b = 16;

3

⇒ b = 5.33;

So when we put value of “a” is -3 then we get value of b is 5.33.

If we put the value of a is -1 then we get:

Put a = -1;

⇒ b = -2a + 10;

3

⇒ b = -2(-1) + 10;

3

⇒ b = 2 + 10;

3

On further solving we get:

⇒ b = 12;

3

⇒ b = 4;

So when we put value of “a” is -1 then we get value of b is 4.

If we put the value of a is 1 then we get:

Put a = 1;

⇒ b = -2a + 10;

3

⇒ b = -2(1) + 10;

3

⇒ b = -2 + 10;

3

On further solving we get:

⇒ b = 8;

3

⇒ b = 2.66;

So when we put value of “a” is 1 then we get value of b is 2.66.

If we put the value of a is 2 then we get:

Put a = 2;

⇒ b = -2a + 10;

3

⇒ b = -2(2) + 10;

3

⇒ b = -4 + 10;

3

On further solving we get:

⇒ b = 6;

3

⇒ b = 2;

So when we put value of “a” is 2 then we get value of b is 3.

If we put the value of a is 2 then we get:

Put a = 4;

⇒ b = -2a + 10;

3

⇒ b = -2(4) + 10;

3

⇒ b = -8 + 10;

3

On further solving we get:

⇒ b = 2;

3

⇒ b = 0.66;

So when we put value of “a” is 2 then we get value of b is 3.

So the coordinates are: (-3, 5.33), (-1, 4), (1, 2.66), (2, 2) and (4, 0.66).

Now we see how to plot the graph with the help of these coordinates:

For plotting the graph we follow the steps given below:

Step1: First we draw two axes, one axis in vertical direction and other axis in horizontal direction.

Step2: We take all the coordinates of ‘a’ on horizontal axis.

Step3: And take coordinates of ‘b’ on vertical axis.

Step4: Then mark the coordinates in horizontal and vertical direction.

Step5: suppose we put the number -3 on horizontal and 5.33 on vertical, and join both the points and we apply same procedure for all remaining coordinates.

Step6: At last we obtained inequality graph.