A rule with x and y
y = ax + b
Tiles again
Back to the tiles: stage 1 has 1 tile, stage 2 has 3, stage 3 has 5, stage 4 has 7. Let x be the stage number and y the number of tiles.
Which rule do you think joins y to x?
What this lesson covers
The idea
A linear relationship between two variables x and y can be expressed in the form y = ax + b.
Tiles again
Back to the tiles: stage 1 has 1 tile, stage 2 has 3, stage 3 has 5, stage 4 has 7. Let x be the stage number and y the number of tiles.
Which rule do you think joins y to x?
- y = 2x − 1
- y = 2x + 1
- y = x + 2
Find the rule
Change a and b in the rule y = ax + b. A row turns green when your rule gives the right y.
y = ax + b
A linear relationship between two variables x and y can be expressed in the form y = ax + b.
Here a and b are fixed numbers. Only x and y change.
- Relationship | a | b
- Tiles: y = 2x − 1 | 2 | −1
- Money left: y = −5x + 100 | −5 | 100
Notes
A linear relationship between x and y can be written y = ax + b, with fixed numbers a and b.
Check yourself
Which equation is of the form y = ax + b?
In y = 4x − 3, what is the value of a?
Answer: 4
a is the number multiplying x: 4.
In y = 4x − 3, what is y when x = 5?
Answer: 17
4 × 5 − 3 = 20 − 3 = 17.
In y = 2x − 1, what is b?
- y = x² + 1. It has x², so it is not linear.
- xy = 4. x and y are multiplied. A linear relationship has y = (a number) × x + (a number).
- y = 3x + 7 — correct. Yes. Here a = 3 and b = 7.
- −1 — correct. Yes. b is the number added on its own, and here it is −1.
- 1. The sign belongs to b: it is −1.
- 2. 2 is a, the number multiplying x.