Step by step
The question
Question: fit line y = 1.25x + 8, x = hours practiced, y = number of songs learned: what does 1.25 mean?
The fit line is y = 1.25x + 8.
We write it big, so we can label it.
1 What the letters mean
y is the predicted number of songs learned.
x is the number of hours practiced.
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 hours practiced: 0, 1 and 2.
0 is where it starts.
x = 0: 1.25 times 0 is 0.
Plus 8 is 8.
x = 1: 1.25 times 1 is 1.25.
Plus 8 is 9.25.
x = 2: 1.25 times 2 is 2.5.
Plus 8 is 10.5.
Look at the values of y: 8, 9.25, 10.5.
Each time x goes up 1, y goes up by 1.25.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
And 8?
At x = 0, 1.25 times 0 is 0.
Only 8 is left: the first number in the table.
So 8 is the predicted number of songs learned at 0 hours practiced: the start.
Where does plus 1.25 each time come from?
From 1.25x: 1.25 times x.
Each extra hour adds one more 1.25.
Careful!
The real points are near the line, not on it.
So 1.25 is a predicted change, not an exact one.
4 Say it in words
So 1.25 means: the predicted number of songs learned goes up 1.25 for each extra hour.
5 Check
Let's check with x = 3.
In words: start at 8, then add 1.25 three times.
We get 11.75.
The equation with x = 3: 1.25 times 3 is 3.75.
Plus 8 gives 11.75 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.