Step by step
The question
Question: The line of best fit is y = 12x + 150, where x is the number of hours of sunshine and y is the number of ice creams sold.
What does 150 mean?
The fit line is y = 12x + 150.
We write it big, so we can label it.
1 What the letters mean
y is the predicted number of ice creams sold.
x is the number of hours of sunshine.
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 of sunshine: 0, 1 and 2.
0 is where it starts.
x = 0: 12 times 0 is 0.
Plus 150 is 150.
x = 1: 12 times 1 is 12.
Plus 150 is 162.
x = 2: 12 times 2 is 24.
Plus 150 is 174.
Look at the values of y: 150, 162, 174.
Each time x goes up 1, y goes up by 12.
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 12 each time come from?
From 12x: 12 times x.
Each extra hour adds one more 12.
And 150?
At x = 0, 12 times 0 is 0.
Only 150 is left: the first number in the table.
So 150 is the predicted number of ice creams sold at 0 hours of sunshine: the start.
Careful!
The real points are near the line, not on it.
So 150 is only a prediction, not an exact value.
4 Say it in words
So 150 means: the predicted number of ice creams sold is 150 at 0 hours of sunshine.
That is the start.
5 Check
Let's check with x = 3.
In words: start at 150, then add 12 three times.
We get 186.
The equation with x = 3: 12 times 3 is 36.
Plus 150 gives 186 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.