Question

Find the rule. Solve for n.
Х
8,9,11,14
Y

10,12,16,n

Rule:

Answer 1

• rule: y = 2x -6
• n = 22

Explanation:

We can look at the ratios of differences between x and y values to determine the nature of the sequence.

x-differences

9 -8 = 1; 11 -9 = 2;

y-differences

12 -10 = 2; 16 -12 = 4;

__

The ratios Δy/Δx are 2/1 = 2 and 4/2 = 2. That is, the points lie on a straight line with slope Δy/Δx = 2.

The y-intercept of the line can be found using the formula ...

b = y -mx

b = 10 -2(8) = -6 . . . . for (x, y) = (8, 10)

So, the rule relating x and y is ...

y = 2x -6

The value of n is ...

n = 2(14) -6 = 22