Identify the explicit function for the sequence in the table. x:1, 2, 3, 4, 5, y: 8, 14, 20, 26, 32,

The explicit function is y = 6x + 2

Explanation:

Since the change in x, Δx is constant and Δx = 1 and also, the change in y, Δy is constant and Δy = 6, we use the equation of a straight line in gradient form.

So, (y - y₁)/(x - x₁) = Δy/Δx where x₁ = 1 and y₁ = 8

So, substituting the values of the variables into the equation, we have

(y - y₁)/(x - x₁) = Δy/Δx

(y - 8)/(x - 1) = 6/1

(y - 8)/(x - 1) = 6

cross-multiplying, we have

(y - 8) = 6(x - 1)

expanding the brackets, we have

y - 8 = 6x - 6

adding 8 to both sides of the equation, we have

y - 8 + 8 = 6x - 6 + 8

y + 0 = 6x + 2

y = 6x + 2

So, the explicit function is y = 6x + 2