Step by step
The question
Question: fit line y = 15x + 20, x = hours worked, y = pay in dollars: what does 15 mean?
The fit line is y = 15x + 20.
We write it big, so we can label it.
1 What the letters mean
y is the predicted pay, in dollars.
x is the number of hours worked.
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 worked: 0, 1 and 2.
0 is where it starts.
x = 0: 15 times 0 is 0.
Plus 20 is 20.
x = 1: 15 times 1 is 15.
Plus 20 is 35.
x = 2: 15 times 2 is 30.
Plus 20 is 50.
Look at the values of y: 20, 35, 50.
Each time x goes up 1, y goes up by 15.
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, 15 times 0 is 0.
Only 20 is left: the first number in the table.
So 20 is the predicted pay at 0 hours worked: the start.
Where does plus 15 each time come from?
From 15x: 15 times x.
Each extra hour adds one more 15.
Careful!
The real points are near the line, not on it.
So 15 is a predicted change, not an exact one.
4 Say it in words
So 15 means: the predicted pay goes up 15 dollars for each extra hour.
5 Check
Let's check with x = 3.
In words: start at 20, then add 15 three times.
We get 65.
The equation with x = 3: 15 times 3 is 45.
Plus 20 gives 65 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.