Step by step
The question
Question: C = 2.5k + 3 is the cost, in dollars, of a taxi ride of k kilometers.
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.
k is the number of kilometers.
2 Make a small table
To see what each number does, we try a few kilometers: 0, 1 and 2.
0 is where it starts.
k = 0: 2.5 times 0 is 0.
Plus 3 is 3.
k = 1: 2.5 times 1 is 2.5.
Plus 3 is 5.5.
k = 2: 2.5 times 2 is 5.
Plus 3 is 8.
Look at the values of C: 3, 5.5, 8.
Each time k goes up 1, C goes up by 2.5.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
Where does plus 2.5 each time come from?
From 2.5k: 2.5 times k.
Each extra kilometer adds one more 2.5.
And 3?
At k = 0, 2.5 times 0 is 0.
Only 3 is left: the first number in the table.
So 3 is the cost of a taxi ride at 0 kilometers: the start.
Careful!
3 is not multiplied by k.
It is there once, even at 0 kilometers.
4 Say it in words
So 3 means: the cost of a taxi ride is 3 dollars at 0 kilometers.
That is the start.
5 Check
Let's check with k = 3.
In words: start at 3, then add 2.5 three times.
We get 10.5.
The equation with k = 3: 2.5 times 3 is 7.5.
Plus 3 gives 10.5 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.