Step by step
The question
Question: The line of best fit is y = 6x + 30, where x is the number of trees planted and y is the number of birds seen.
What does 6 mean?
The fit line is y = 6x + 30.
We write it big, so we can label it.
1 What the letters mean
y is the predicted number of birds seen.
x is the number of trees planted.
A fit line is drawn through data: real numbers someone collected, shown as points.
The line only predicts: the real points are near it, not on it.
2 Make a small table
To see what each number does, we try a few trees planted: 0, 1 and 2.
0 is where it starts.
x = 0: 6 times 0 is 0.
Plus 30 is 30.
x = 1: 6 times 1 is 6.
Plus 30 is 36.
x = 2: 6 times 2 is 12.
Plus 30 is 42.
Look at the values of y: 30, 36, 42.
Each time x goes up 1, y goes up by 6.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
And 30?
At x = 0, 6 times 0 is 0.
Only 30 is left: the first number in the table.
So 30 is the predicted number of birds seen at 0 trees planted: the start.
Where does plus 6 each time come from?
From 6x: 6 times x.
Each extra tree adds one more 6.
Careful!
The real points are near the line, not on it.
So 6 is a predicted change, not an exact one.
4 Say it in words
So 6 means: the predicted number of birds seen goes up 6 for each extra tree.
5 Check
Let's check with x = 3.
In words: start at 30, then add 6 three times.
We get 48.
The equation with x = 3: 6 times 3 is 18.
Plus 30 gives 48 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.