**Matching graphs to situations :**

In this section, we are going to see, how the given situations can be matched to their respective graphs.

**Example 1 :**

George, Jacob and Micheal are studying 100 words for a spelling bee.

(1) George started by learning how to spell many words each day but then learned fewer and fewer words each day.

(2) Jacob learned how to spell the same number of words each day.

(3) Micheal started by learning how to spell the same number of words each day but then learned a greater number of words each day.

The graphs matching to the above situations are given below, but not in the order as situations given above.

Tell which graph corresponds to each situation.

**Solution : **

**Step 1 : **

Graph A shows a constant rate. This means, the student learned how to spell the same number of words each day.

It exactly matches the situation (2).

**Step 2 :**

Graph B begins with a shallow curve and gets steeper. This means, the student learned a few words at first, and then learned more at the end.

It exactly matches the situation (3).

**Step 3 :**

Graph C begins with a steep curve that gets more shallow. This means, the student learned many words at first, and then learned fewer words at the end.

It exactly matches the situation (1).

**Example 1 :**

The speeds of three people A, B and C who are riding snowmobiles.

(1) Person A steadily increases his speed through most of his ride. Then the person A slows down as he nears some trees.

(2) Person B begins his ride slowly but then stops to talk with some friends. After a few minutes, he continues his ride, gradually increasing his speed.

(3) Person C steadily increases his speed for some time, then he maintains the constant rate.

The graphs matching to the above situations are given below, but not in the order as situations given above.

Tell which graph corresponds to each situation.

**Solution : **

**Step 1 :**

Graph 1 starts with a positive slope and slope becomes zero. This means, the person steadily increases his speed for some time, then he maintains the constant rate.

It exactly matches the situation of the person C.

**Step 2 :**

Graph 2 starts with a positive slope, then the slope becomes negative, zero and positive. This means, the person begins his ride slowly but then stops. After a few minutes, he continues his ride, gradually increasing his speed.

It exactly matches the situation of the person B.

**Step 3 :**

Graph 3 starts with a positive slope, then the slope becomes negative. This means, the person steadily increases his speed, then the person slows down.

It exactly matches the situation of the person A.

After having gone through the stuff given above, we hope that the students would have understood "Matching graphs to situations".

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