Step by step
The question
Question: The line of best fit is y = −1.5x + 90, where x is the number of hours of TV watched and y is the test score.
What does 1.5 mean?
The fit line is y = −1.5x + 90.
We write it big, so we can label it.
1 What the letters mean
y is the predicted test score.
x is the number of hours of TV watched.
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 of TV watched: 0, 1 and 2.
0 is where it starts.
x = 0: −1.5 times 0 is 0.
Plus 90 is 90.
x = 1: −1.5 times 1 is −1.5.
Plus 90 is 88.5.
x = 2: −1.5 times 2 is −3.
Plus 90 is 87.
Look at the values of y: 90, 88.5, 87.
Each time x goes up 1, y goes down by 1.5.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
And 90?
At x = 0, −1.5 times 0 is 0.
Only 90 is left: the first number in the table.
So 90 is the predicted test score at 0 hours of TV watched: the start.
Where does minus 1.5 each time come from?
From −1.5x: −1.5 times x.
Each extra hour takes away one more 1.5.
Careful!
The real points are near the line, not on it.
So 1.5 is a predicted change, not an exact one.
4 Say it in words
So 1.5 means: the predicted test score goes down 1.5 for each extra hour.
5 Check
Let's check with x = 3.
In words: start at 90, then take away 1.5 three times.
We get 85.5.
The equation with x = 3: −1.5 times 3 is −4.5.
Plus 90 gives 85.5 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.