Question

find the rule and complete the table.
in out
80
83 45
86 48
91 53
93
99 61

Explanation:

Step1: Find the difference between In - values

The differences between consecutive In - values are: \(83 - 80=3\), \(86 - 83 = 3\), \(91 - 86=5\), \(93 - 91 = 2\), \(99 - 93=6\).
The differences between consecutive Out - values are: \(48 - 45 = 3\), \(53 - 48 = 5\), \(61 - 53=8\).
Let's assume the rule is of the form \(y=ax + b\).
We take two points \((83,45)\) and \((86,48)\).
The slope \(a=\frac{48 - 45}{86 - 83}=\frac{3}{3}=1\).
Using the point - slope form \(y - y_1=a(x - x_1)\) with the point \((83,45)\) and \(a = 1\), we have \(y-45=1\times(x - 83)\), so \(y=x - 38\).

Step2: Calculate the missing values

For \(x = 80\), \(y=80-38 = 42\).
For \(x = 93\), \(y=93-38 = 55\).

Answer:

The first blank is 42 and the second blank is 55.