Identify the explicit function for the sequence in the table. x:1, 2, 3, 4, 5, y: 8, 14, 20, 26, 32,
zhuklara [117]
Answer:
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
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