Step by step
The question
Question: fit line y = −4x + 70, x = days of rain, y = park visitors: what does 4 mean?
The fit line is y = −4x + 70.
We write it big, so we can label it.
1 What the letters mean
y is the predicted park visitors.
x is the number of days of rain.
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 days of rain: 0, 1 and 2.
0 is where it starts.
x = 0: −4 times 0 is 0.
Plus 70 is 70.
x = 1: −4 times 1 is −4.
Plus 70 is 66.
x = 2: −4 times 2 is −8.
Plus 70 is 62.
Look at the values of y: 70, 66, 62.
Each time x goes up 1, y goes down by 4.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
And 70?
At x = 0, −4 times 0 is 0.
Only 70 is left: the first number in the table.
So 70 is the predicted park visitors at 0 days of rain: the start.
Where does minus 4 each time come from?
From −4x: −4 times x.
Each extra day takes away one more 4.
Careful!
The real points are near the line, not on it.
So 4 is a predicted change, not an exact one.
4 Say it in words
So 4 means: the predicted park visitors goes down 4 for each extra day.
5 Check
Let's check with x = 3.
In words: start at 70, then take away 4 three times.
We get 58.
The equation with x = 3: −4 times 3 is −12.
Plus 70 gives 58 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.