Step by step
The question
Question: fit line y = 0.5x + 60, x = minutes of exercise, y = heart rate: what does 60 mean?
The fit line is y = 0.5x + 60.
We write it big, so we can label it.
1 What the letters mean
y is the predicted heart rate.
x is the number of minutes of exercise.
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 of exercise: 0, 1 and 2.
0 is where it starts.
x = 0: 0.5 times 0 is 0.
Plus 60 is 60.
x = 1: 0.5 times 1 is 0.5.
Plus 60 is 60.5.
x = 2: 0.5 times 2 is 1.
Plus 60 is 61.
Look at the values of y: 60, 60.5, 61.
Each time x goes up 1, y goes up by 0.5.
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 0.5 each time come from?
From 0.5x: 0.5 times x.
Each extra minute adds one more 0.5.
And 60?
At x = 0, 0.5 times 0 is 0.
Only 60 is left: the first number in the table.
So 60 is the predicted heart rate at 0 minutes of exercise: the start.
Careful!
The real points are near the line, not on it.
So 60 is only a prediction, not an exact value.
4 Say it in words
So 60 means: the predicted heart rate is 60 at 0 minutes of exercise.
That is the start.
5 Check
Let's check with x = 3.
In words: start at 60, then add 0.5 three times.
We get 61.5.
The equation with x = 3: 0.5 times 3 is 1.5.
Plus 60 gives 61.5 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.