Question

17.
input values
3
6
9
12
15
output values
11
9
7
5
3
constant rate of change (slope):
equation:
18.

Explanation:

Step1: Find the slope

We can take two points from the input and output values. Let's take \((x_1, y_1)=(3, 11)\) and \((x_2, y_2)=(6, 9)\). The formula for slope \(m\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
So, \(m=\frac{9 - 11}{6 - 3}=\frac{-2}{3}\).

Step2: Find the equation of the line

We use the point - slope form \(y - y_1=m(x - x_1)\). Using the point \((3, 11)\) and \(m =-\frac{2}{3}\):
\(y - 11=-\frac{2}{3}(x - 3)\)
Expand the right - hand side: \(y-11 =-\frac{2}{3}x + 2\)
Add 11 to both sides: \(y=-\frac{2}{3}x+2 + 11\), so \(y =-\frac{2}{3}x + 13\)

Answer:

Constant rate of change (slope): \(-\frac{2}{3}\)
Equation: \(y =-\frac{2}{3}x + 13\)