Linear equations

Linear equations are all equations that have the following form: y = ax + b    

x is called independent variable    y is called dependent variable      a and b are called constant.





For examples, y = 2x + 5 with a = 2 and b = 5     y = -3x + 2 with a = -3 and b = 2

y = 4x + - 1 with a = 4 and b = -1

Real life examples, or word problems on linear equations are numerous.

Consider the following two examples:

Example #1:

I am thinking of a number. If I add 2 to that number, I will get 5. What is the number?

Although it may be fairly easy to guess that the number is 3, you can model the situation above with an equation

Let x be the number in my mind.

Add 2 to x to get 5

Adding 2 to x to get 5 means that whatever x is, when I add 2 to x, it has to equal to 5

The equation is

2 + x = 5

Example #2 :

Soon or later, all of us use the service of a taxi driver

Taxi drivers usually charge a an initial fixed fee as part of using their services. Then, for each mileage, they charge a certain amount

Say for instance, the initial fee is 4 dollars and each mileage cost 2 dollars

The total cost can be modeled with an equation that is linear.

Let y be the total cost

Let N be number of mileage

Total cost = 4 + cost for N miles

Notice that cost for N miles = N ×2

Therefore, y = 4 + N × 2

Say for instance, a taxi driver takes you to a distance of 20 miles, how much money do you have to pay using y = 4 + N × 2 ?

When N = 20, Y = 4 + 20 × 2 = 4 + 40 = 44 dollars

Now, let's ask the question the other way around!

If you pay 60 dollars, how far did the taxi driver took you?

This time y = 60

Replacing 60 into the equation gives you the following equation:

60 = 4 + N × 2

It is not obvious to see that N = 28.

That is why it is important to learn to solve linear equations!





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