Step by step
The question
Question: fit line y = −2x + 95, x = absences, y = final grade: what does 2 mean?
The fit line is y = −2x + 95.
We write it big, so we can label it.
1 What the letters mean
y is the predicted final grade.
x is the number of absences.
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 absences: 0, 1 and 2.
0 is where it starts.
x = 0: −2 times 0 is 0.
Plus 95 is 95.
x = 1: −2 times 1 is −2.
Plus 95 is 93.
x = 2: −2 times 2 is −4.
Plus 95 is 91.
Look at the values of y: 95, 93, 91.
Each time x goes up 1, y goes down by 2.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
And 95?
At x = 0, −2 times 0 is 0.
Only 95 is left: the first number in the table.
So 95 is the predicted final grade at 0 absences: the start.
Where does minus 2 each time come from?
From −2x: −2 times x.
Each extra absence takes away one more 2.
Careful!
The real points are near the line, not on it.
So 2 is a predicted change, not an exact one.
4 Say it in words
So 2 means: the predicted final grade goes down 2 for each extra absence.
5 Check
Let's check with x = 3.
In words: start at 95, then take away 2 three times.
We get 89.
The equation with x = 3: −2 times 3 is −6.
Plus 95 gives 89 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.