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!