Step by step
The question
Question: fit line y = 3x + 12, x = days of practice, y = number of baskets made: what does 3 mean?
The fit line is y = 3x + 12.
We write it big, so we can label it.
1 What the letters mean
y is the predicted number of baskets made.
x is the number of days of practice.
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 days of practice: 0, 1 and 2.
0 is where it starts.
x = 0: 3 times 0 is 0.
Plus 12 is 12.
x = 1: 3 times 1 is 3.
Plus 12 is 15.
x = 2: 3 times 2 is 6.
Plus 12 is 18.
Look at the values of y: 12, 15, 18.
Each time x goes up 1, y 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 12?
At x = 0, 3 times 0 is 0.
Only 12 is left: the first number in the table.
So 12 is the predicted number of baskets made at 0 days of practice: the start.
Where does plus 3 each time come from?
From 3x: 3 times x.
Each extra day adds one more 3.
Careful!
The real points are near the line, not on it.
So 3 is a predicted change, not an exact one.
4 Say it in words
So 3 means: the predicted number of baskets made goes up 3 for each extra day.
5 Check
Let's check with x = 3.
In words: start at 12, then add 3 three times.
We get 21.
The equation with x = 3: 3 times 3 is 9.
Plus 12 gives 21 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.