Answer:
The equation that represents the relation between the figure number, x, and the number of the tiles, y is y = 2x + 1
Explanation:
The slope-intercept form of the equation is y = m x + b, where
- m is the slope ⇒ constant rate of change
In the given pattern
∵ x represents the figure number
∵ y represents the number of tiles
∵ At x = 1, y = 3
∵ At x = 2, y = 5
∵ At x = 3, y = 7
∵ 5 - 3 = 2 and 7 - 5 = 2
→ That means the constant rate of change is 2
∴ m = 2
→ Substitute it in the form of the equation above
∴ y = 2x + b
→ To find b substitute x and y by the first figure
∵ x = 1 and y = 3
∴ 3 = 2(1) + b
∴ 3 = 2 + b
→ Subtract 2 from both sides to find b
∴ 3 - 2 = 2 - 2 + b
∴ 1 = b
→ Substitute it in the equation
∴ y = 2x + 1
The equation that represents the relation between the figure number, x, and the number of the tiles, y is y = 2x + 1