Step by step
The question
Question: fit line y = 2x + 10, x = cups of water given, y = plant height in centimeters: what does 10 mean?
The fit line is y = 2x + 10.
We write it big, so we can label it.
1 What the letters mean
y is the predicted plant height, in centimeters.
x is the number of cups of water given.
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 cups of water given: 0, 1 and 2.
0 is where it starts.
x = 0: 2 times 0 is 0.
Plus 10 is 10.
x = 1: 2 times 1 is 2.
Plus 10 is 12.
x = 2: 2 times 2 is 4.
Plus 10 is 14.
Look at the values of y: 10, 12, 14.
Each time x goes up 1, y goes up by 2.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
Where does plus 2 each time come from?
From 2x: 2 times x.
Each extra cup adds one more 2.
And 10?
At x = 0, 2 times 0 is 0.
Only 10 is left: the first number in the table.
So 10 is the predicted plant height at 0 cups of water given: the start.
Careful!
The real points are near the line, not on it.
So 10 is only a prediction, not an exact value.
4 Say it in words
So 10 means: the predicted plant height is 10 centimeters at 0 cups of water given.
That is the start.
5 Check
Let's check with x = 3.
In words: start at 10, then add 2 three times.
We get 16.
The equation with x = 3: 2 times 3 is 6.
Plus 10 gives 16 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.