Step by step
The question
Question: fit line y = 0.6x + 35, x = minutes read, y = reading score: what does 35 mean?
The fit line is y = 0.6x + 35.
We write it big, so we can label it.
1 What the letters mean
y is the predicted reading score.
x is the number of minutes read.
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 minutes read: 0, 1 and 2.
0 is where it starts.
x = 0: 0.6 times 0 is 0.
Plus 35 is 35.
x = 1: 0.6 times 1 is 0.6.
Plus 35 is 35.6.
x = 2: 0.6 times 2 is 1.2.
Plus 35 is 36.2.
Look at the values of y: 35, 35.6, 36.2.
Each time x goes up 1, y goes up by 0.6.
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 0.6 each time come from?
From 0.6x: 0.6 times x.
Each extra minute adds one more 0.6.
And 35?
At x = 0, 0.6 times 0 is 0.
Only 35 is left: the first number in the table.
So 35 is the predicted reading score at 0 minutes read: the start.
Careful!
The real points are near the line, not on it.
So 35 is only a prediction, not an exact value.
4 Say it in words
So 35 means: the predicted reading score is 35 at 0 minutes read.
That is the start.
5 Check
Let's check with x = 3.
In words: start at 35, then add 0.6 three times.
We get 36.8.
The equation with x = 3: 0.6 times 3 is 1.8.
Plus 35 gives 36.8 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.