Question

A function contains the 5 ordered pairs below (x,y). Four of the points as given below
(1,3) (2,5), (6, 13), (9,27)
Question:
Identify a 5th point that would maintain the function.
*Provide an ordered pair
*Explain why this maintains the function

Answer 1

A 5th point that would maintain the function is (11, 31)

Coordinate pairs of a function

Given the following pairs of coordinates

Four of the points are given as (1,3) (2,5), (6, 13), (9,27)

Using the coordinates  (1,3) (2,5), to determine the slope

$Slope=\frac{5-3}{2-1} = \frac{13-5}{6-2}=2$

Let the required coordinate be (x, y) to have:
$2 = \frac{y - 27}{x - 9}$

Since the x coordinate of (9, 27) is greater than 8, hence the best x-coordinate will be 11. Substitute to get the y-coordinate

$2 = \frac{y - 27}{11- 9}\\2(2) = y - 27 \\4 = y - 27\\y=27 + 4\\y=31$

Hence a 5th point that would maintain the function is (11, 31)

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