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
The following are all examples of such equations:
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 equations!
Integers
Adding integers
Subtracting integers
Multiplying integers
Division of integers
Variables in algebra
Linear equations
Solving equations using addition
Solving equations using subtraction
Solving multiplication equations
Solving two step equations
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