Step by step
The question
Question: fit line y = 4x + 50, x = weeks of training, y = number of laps swum: what does 4 mean?
The fit line is y = 4x + 50.
We write it big, so we can label it.
1 What the letters mean
y is the predicted number of laps swum.
x is the number of weeks of training.
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 weeks of training: 0, 1 and 2.
0 is where it starts.
x = 0: 4 times 0 is 0.
Plus 50 is 50.
x = 1: 4 times 1 is 4.
Plus 50 is 54.
x = 2: 4 times 2 is 8.
Plus 50 is 58.
Look at the values of y: 50, 54, 58.
Each time x goes up 1, y goes up by 4.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
And 50?
At x = 0, 4 times 0 is 0.
Only 50 is left: the first number in the table.
So 50 is the predicted number of laps swum at 0 weeks of training: the start.
Where does plus 4 each time come from?
From 4x: 4 times x.
Each extra week adds one more 4.
Careful!
The real points are near the line, not on it.
So 4 is a predicted change, not an exact one.
4 Say it in words
So 4 means: the predicted number of laps swum goes up 4 for each extra week.
5 Check
Let's check with x = 3.
In words: start at 50, then add 4 three times.
We get 62.
The equation with x = 3: 4 times 3 is 12.
Plus 50 gives 62 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.