Representation of Phenomena - Examples, Exercises and Solutions

Question Types:
Representation of Phenomena: Linking function properties to its representation

A linear function describes the relationship between X X and Y Y .
Therefore, we can represent all sorts of different phenomena in life with the help of the linear function.
The representation of phenomena with the help of linear functions is expressed in mathematics in word problems, using graphs of the functions.
Thus, we can find the various relationships between the functions.

Representing phenomena using linear functions actually allows us to simplify many word questions using a simple linear graph. From the graph, we can very easily calculate the slope, which is actually the rate of change and even many other parameters.

A - Representation of Phenomena Using Linear Functions

Detailed explanation

Suggested Topics to Practice in Advance

  1. Function
  2. Linear Function
  3. The Linear Function y=mx+b
  4. Slope in the Function y=mx
  5. Positive and Negativity of a Linear Function
  6. Finding a Linear Equation
  7. Graphs of Direct Proportionality Functions

Practice Representation of Phenomena

Question 1

The graph below depicts the price of apples relative to the quantity.

How many kg of apples can you buy for $9?

–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111121212131313141414151515161616171717181818191919202020111222333444555666777888999101010111111121212kg de manzanasPrecio

Question 2

The graph below depicts the price of apples relative to the quantity.

What is the price of 7 kg of apples?

–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111121212131313141414151515161616171717181818191919202020111222333444555666777888999101010111111121212kg de manzanasPrecio

Question 3

The graph below depicts the price of tomatoes as a function of quantity, with each line representing the prices at different shops.

Where is it cheaper to buy 7 kg of tomatoes?

–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111121212131313141414151515161616171717181818191919–1–1–1111222333444555666777888999101010111111kg de tomatesPrecio

Question 4

There are two water containers. The first container is empty, whilst the second contains 48 liters of water.

After how many minutes will the second container be completely full?

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Question 5

A car leaves Madrid for Barcelona. During the journey, the driver has a break.

For how many hours did the driver rest?

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Examples with solutions for Representation of Phenomena

Exercise #1

The graph below depicts the price of apples relative to the quantity.

How many kg of apples can you buy for $9?

–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111121212131313141414151515161616171717181818191919202020111222333444555666777888999101010111111121212kg de manzanasPrecio

Video Solution

Step-by-Step Solution

Let's look at the Y-axis which shows us the price data. Locate 9 dollars - and mark a point.

From this point, we'll draw a vertical line until we meet the straight line.

Now let's look at the X-axis which shows us the quantity in kg.

We'll draw a line from the point where we reached the Y-axis to the straight line, towards the X-axis and determine the weight: 8 kg.

Answer

8

Exercise #2

The graph below depicts the price of apples relative to the quantity.

What is the price of 7 kg of apples?

–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111121212131313141414151515161616171717181818191919202020111222333444555666777888999101010111111121212kg de manzanasPrecio

Video Solution

Step-by-Step Solution

Let's look at the X-axis which shows us the weight. Locate 7 kg - and mark a point.

From this point, we'll draw a vertical line until we meet the straight line.

Now let's look at the Y-axis which shows us the price.

We'll draw a line from the point where we reached the X-axis to the straight line, towards the Y-axis and determine the price: 8 dollars.

Answer

8

Exercise #3

The graph below depicts the price of tomatoes as a function of quantity, with each line representing the prices at different shops.

Where is it cheaper to buy 7 kg of tomatoes?

–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111121212131313141414151515161616171717181818191919–1–1–1111222333444555666777888999101010111111kg de tomatesPrecio

Video Solution

Step-by-Step Solution

Let's look at the red line:

The X-axis shows us the quantity, we'll locate 7 kg and from it draw a vertical line to the line - mark a point.

From this point we'll draw a horizontal line to the Y-axis which shows the price and we'll see that 7 kg costs 8 NIS.

Let's look at the blue line:

The X-axis shows us the quantity, we'll locate 7 kg and from it draw a vertical line to the line - mark a point.

From this point we'll draw a horizontal line to the Y-axis which shows the price and we'll see that 7 kg costs 10 NIS.

Therefore it's better to buy at the red store, it's cheaper.

Answer

In the red shop

Exercise #4

There are two water containers. The first container is empty, whilst the second contains 48 liters of water.

After how many minutes will the second container be completely full?

Minutos000222444666888101010121212141414161616181818202020222222242424262626282828Litros484848565656646464727272808080888888969696104104104112112112120120120128128128136136136144144144152152152160160160AAABBB

Step-by-Step Solution

Let's look at the blue line that represents the second container.

Notice that it will be full at the point where it starts to become a continuous line.

Let's draw a vertical line from this point to the X-axis which marks the minutes.

We can see that the line reaches 22, meaning the container will be full in 22 minutes.

Answer

22 minutes

Exercise #5

A car leaves Madrid for Barcelona. During the journey, the driver has a break.

For how many hours did the driver rest?

Hora000111222333444555666777888999101010111111121212131313141414151515161616171717181818191919202020km000101010202020303030404040505050606060707070808080909090100100100110110110120120120130130130140140140

Video Solution

Answer

6