Step by step
The question
Question: C = 3m + 2 is the cost, in dollars, of a taxi ride of m miles.
What does 3 mean?
We write the equation big, so we can label it.
1 What the letters mean
C is the cost of a taxi ride, in dollars.
m is the number of miles.
2 Make a small table
To see what each number does, we try a few miles: 0, 1 and 2.
0 is where it starts.
m = 0: 3 times 0 is 0.
Plus 2 is 2.
m = 1: 3 times 1 is 3.
Plus 2 is 5.
m = 2: 3 times 2 is 6.
Plus 2 is 8.
Look at the values of C: 2, 5, 8.
Each time m goes up 1, C goes up by 3.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
And 2?
At m = 0, 3 times 0 is 0.
Only 2 is left: the first number in the table.
So 2 is the cost of a taxi ride at 0 miles: the start.
Where does plus 3 each time come from?
From 3m: 3 times m.
Each extra mile adds one more 3.
Careful!
3 is multiplied by m, so each mile adds another 3.
The start is the number alone.
4 Say it in words
So 3 means: the cost of a taxi ride goes up 3 dollars for each extra mile.
5 Check
Let's check with m = 3.
In words: start at 2, then add 3 three times.
We get 11.
The equation with m = 3: 3 times 3 is 9.
Plus 2 gives 11 too.
So the meaning is right!
Let's look back.
First: what the letters mean.
Then: make a small table.
Then: find the numbers in the table.
Then: say it in words.
Last: check.