Step by step
The question
Question: fit line y = 8x + 20, x = ads shown, y = sales in dollars: what does 8 mean?
The fit line is y = 8x + 20.
We write it big, so we can label it.
1 What the letters mean
y is the predicted sales, in dollars.
x is the number of ads shown.
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 ads shown: 0, 1 and 2.
0 is where it starts.
x = 0: 8 times 0 is 0.
Plus 20 is 20.
x = 1: 8 times 1 is 8.
Plus 20 is 28.
x = 2: 8 times 2 is 16.
Plus 20 is 36.
Look at the values of y: 20, 28, 36.
Each time x goes up 1, y goes up by 8.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
And 20?
At x = 0, 8 times 0 is 0.
Only 20 is left: the first number in the table.
So 20 is the predicted sales at 0 ads shown: the start.
Where does plus 8 each time come from?
From 8x: 8 times x.
Each extra ad adds one more 8.
Careful!
The real points are near the line, not on it.
So 8 is a predicted change, not an exact one.
4 Say it in words
So 8 means: the predicted sales go up 8 dollars for each extra ad.
5 Check
Let's check with x = 3.
In words: start at 20, then add 8 three times.
We get 44.
The equation with x = 3: 8 times 3 is 24.
Plus 20 gives 44 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.