**Write inequalities from graphs :**

Writing inequalities from graph is straight opposite process of graphing inequalities.

Before going to learn how to write inequalities, we must know about two shapes.

Let us see some example problems based on the above concept.

**Example 1 :**

Write the inequality for the graph given below.

**Solution :**

**In the above graph, we find the filled circle. So we have to use the sign **≤ or ≥.

Now we have to look into the shaded portion. Since the shaded region is in left hand side from the filled circle, we have to use the sign "≤ ".

Hence the correct inequality of the above graph is x ≤ 4.

**Example 2 :**

Write the inequality for the graph given below.

**Solution :**

**In the above graph, we find the unfilled circle. So we have to use the sign <** or >.

Now we have to look into the shaded portion. Since the shaded region is in right hand side from the unfilled circle, we have to use the sign "> ".

Hence the correct inequality of the above graph is x > -6.

**Example 3 :**

Write the inequality for the graph given below.

**Solution :**

**In the above graph, we find the unfilled circle. So we have to use the sign <** or >.

Now we have to look into the shaded portion. Since the shaded region is in left hand side from the unfilled circle, we have to use the sign "<".

Hence the correct inequality of the above graph is x < 1.

**Example 4 :**

Write the inequality for the graph given below.

**Solution :**

**In the above graph, we find the unfilled circle. So we have to use the sign **≤ or ≥.

Now we have to look into the shaded portion. Since the shaded region is in right hand side from the unfilled circle, we have to use the sign "≥".

Hence the correct inequality of the above graph is x ≥ 1.

To find linear inequalities in two variables from graph, first we have to find two information from the graph.

(i) Slope

(ii) y -intercept

By using the above two informations we can easily get a linear linear equation in the form y = mx + b.

Here "m" stands for slope and "b" stands for y-intercept.

Now we have to notice whether the given line is solid line or dotted line.

- If the graph contains the dotted line, then we have to use one of the signs < or >.
- If the graph contains the solid line, then we have to use one of the signs ≤ or ≥.

**Example 5 :**

Write the inequality for the graph given below.

**Solution :**

From the above graph, first let us find the slope and y-intercept.

Rise = -3 and Run = 1

Slope = -3/1 ==> -3

y-intercept = 4

So, the equation of the given line is y = -3x + 4. But we need to use inequality which satisfies the shaded region.

Since the graph contains solid line, we have to use one of the signs ≤ or ≥.

To fix the correct sign, let us take a point from the shaded region.

Take the point (2, 1) and apply it in the equation y = -3x + 4

1 = -3(2) + 4

1 = -6 + 4

1 = - 2

Here 1 is greater than -2, so we have to choose the sign ≥ instead of equal sign in the equation y = -3x + 4

Hence the required equation is y ≥ -3x + 4.

After having gone through the stuff given above, we hope that the students would have understood "Write inequalities from graphs".

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