Step by step
The question
Question: The line of best fit is y = −0.05x + 12, where x is the number of miles driven and y is the gas left in gallons.
What does 12 mean?
The fit line is y = −0.05x + 12.
We write it big, so we can label it.
1 What the letters mean
y is the predicted gas left, in gallons.
x is the number of miles driven.
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 miles driven: 0, 1 and 2.
0 is where it starts.
x = 0: −0.05 times 0 is 0.
Plus 12 is 12.
x = 1: −0.05 times 1 is −0.05.
Plus 12 is 11.95.
x = 2: −0.05 times 2 is −0.1.
Plus 12 is 11.9.
Look at the values of y: 12, 11.95, 11.9.
Each time x goes up 1, y goes down by 0.05.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
Where does minus 0.05 each time come from?
From −0.05x: −0.05 times x.
Each extra mile takes away one more 0.05.
And 12?
At x = 0, −0.05 times 0 is 0.
Only 12 is left: the first number in the table.
So 12 is the predicted gas left at 0 miles driven: the start.
Careful!
The real points are near the line, not on it.
So 12 is only a prediction, not an exact value.
4 Say it in words
So 12 means: the predicted gas left is 12 gallons at 0 miles driven.
That is the start.
5 Check
Let's check with x = 3.
In words: start at 12, then take away 0.05 three times.
We get 11.85.
The equation with x = 3: −0.05 times 3 is −0.15.
Plus 12 gives 11.85 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.