# Representation of Phenomena Using Linear Functions

🏆Practice representation of phenomena

A linear function describes the relationship between $X$ and $Y$.
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.

## Test yourself on representation of phenomena!

The graph below represents the price of apples depending on the quantity.

What is the price of 7 kg of apples?

## Example of representing phenomena using linear functions

At $10$ in the morning, truck $A$ left the factory in Valencia for the factory in Madrid, a distance of $380$ km.
At the same time, truck $B$ left the factory in Madrid for the factory in Valencia.

The two trucks were supposed to meet somewhere along the way.
The figure in front of you shows graphs that describe the position of the drivers at any time during the journey.

## What does each marked point on the graph mean?

Solution:
Let's first look at the points on the blue graph:
We can associate the blue graph with truck $A$ since we see it started from the point ($0,0$).
Truck $A$ departed from a point which is the distance from Valencia was $0$ km, meaning it left from Valencia. Therefore, the point ($0,0$) is the starting point of truck $A$. The second point on the blue graph: ( $12,380$) represents the arrival point of truck $A$ in Madrid.
After 12 hours and after $380$ km.

Now let's look at the points on the purple graph:
($3.8,0$) this point represents truck $B$ and shows us that after $3.8$ hours, the truck arrived in Valencia: its distance from Valencia was $0$ km.
(0,380 ): represents truck $B$ and shows us its starting point where it had not yet begun to travel and its distance to Valencia was $380$ km.

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## When and at what distance did the two trucks meet?

To answer this question, we will have to find the equations of the two lines and solve a system of equations with two variables.

We will find the equation of truck $A$ with the help of the $2$ given points.
We will do the same for truck $B$.
The two equations we obtain will form a system of equations with two variables. We will solve the system and obtain the meeting point between the two trucks.

In terms of time, we will obtain the value $X$ and in terms of distance from Valencia, we will obtain the value $Y$.

If you are interested in this article, you might also be interested in the following articles:

Linear function

Graphical representation of a function that represents a direct proportionality

The linear function y=mx+b

Finding linear equation

Positivity and negativity of a linear function

In the blog of Tutorela you will find a variety of articles about mathematics.

## Examples and exercises with solutions for representing phenomena using linear functions

### Exercise #1

The graph below represents the price of apples depending on the quantity.

What is the price of 7 kg of apples?

8

### Exercise #2

The graph below depicts the price of apples depending on the quantity.

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

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?

In the red shop

### Exercise #4

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

For how many hours did the driver rest?