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SO YOU WANT TO WRITE AN EQUATION...


y = mx + b  or  ax + b = c

 

Though it's not entirely universal, writing equations from word problems usually boil down to five simple rules. Let's uncover what they are!

A little background first...most linear equations (degree of 1) can be written in the form y = mx + b or, in certain circles, ax + b = c. For this demonstration and since they are essentially the same equation, we will use y = mx + b because it has many different applications using those specific variables. For the super intellects, I will have the correlation between the two forms at the end of this post.
 

We break down the equation as follows:
y = result/solution/answer
m = coefficient; can be negative or positive
x = variable/input             
b = starting point/beginning value
 

Depending on what's happening to m, y and b, we will solve for some value of x.
 

5 Rules of Writing an Equation from a Real World Situation
 

1. Define the variable. ( x )

  • What is the unknown? What are you solving for? This is the purpose of the variable above, this is what we need to find the value of.

 

2. What is the starting value? ( b )

  • What is the constant in the word problem? Can be negative or positive. This may come in a variety of ways: beginning balance in a bank, starting number of stamps in a collection, cost of 3 slices of pizza, etc. 

 

3. How is the starting value going to change? ( -m or +m)

  • Will it increase (positive coefficient) or decrease (negative coefficient)? This will be directly related to the information found for the starting value: is the bank balance increasing/decreasing, is the stamp collection increasing/decreasing, are you adding more food to your order or removing food from the order, etc.

 

4. What is the end goal? ( y )

  • Again, directly related to starting value and change in starting value: what is the end balance in the bank required? What number of stamps are desired? How much money is available to spend on food and drinks?

 

5. Build the equation using the form: y = mx + b 

  • Substitute the values found in steps 1 - 4.

 

Example: 

Senator Rohman is purchasing Arabian war horses to supplement her current stable. The stable hand reports that the horseflesh numbers 27. The senator must hire out a ship to bring the Arabian horses; this will take about a month and they can only travel three at a time. How many months before Senator Rohman can wage war against Caesar with an army of 65 Arabian horses? 

 

Break it down:

 

Step 1: Let x be the number of months it takes to get the horses. FIND VALUE OF X

Step 2: Starting with 27 horses (positive value). B = + 27

Step 3: The starting value will increase by 3. M = POSITIVE 3

Step 4: The senator wants 65 horses. y = 65

Step 5: 65 = 3x + 27 

 

When we solve this equation, 3x + 27 = 65, using inverse operations, we find that x = 12.666666... or one year and a little over 3 weeks.

 

All done in five easy steps! 

 

Carpe Diem! 

 

~ Rohman

 

 

 

y = mx + b    vs    ax + b = c

 

 When first introduced to equation forms, we use ax + b = c. As we move into linear equations and functions, we begin using y = mx + b. The two are really one and the same, because: y, the result, can be written as c; m, the coefficient, can be written as a; x is still used in both forms and so is b. 

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