Step by step
The question
Question: fit line y = 0.2x + 1, x = miles driven, y = gallons used: what does 0.2 mean?
The fit line is y = 0.2x + 1.
We write it big, so we can label it.
1 What the letters mean
y is the predicted gallons used.
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: 0.2 times 0 is 0.
Plus 1 is 1.
x = 1: 0.2 times 1 is 0.2.
Plus 1 is 1.2.
x = 2: 0.2 times 2 is 0.4.
Plus 1 is 1.4.
Look at the values of y: 1, 1.2, 1.4.
Each time x goes up 1, y goes up by 0.2.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
And 1?
At x = 0, 0.2 times 0 is 0.
Only 1 is left: the first number in the table.
So 1 is the predicted gallons used at 0 miles driven: the start.
Where does plus 0.2 each time come from?
From 0.2x: 0.2 times x.
Each extra mile adds one more 0.2.
Careful!
The real points are near the line, not on it.
So 0.2 is a predicted change, not an exact one.
4 Say it in words
So 0.2 means: the predicted gallons used go up 0.2 for each extra mile.
5 Check
Let's check with x = 3.
In words: start at 1, then add 0.2 three times.
We get 1.6.
The equation with x = 3: 0.2 times 3 is 0.6.
Plus 1 gives 1.6 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.