Question

1. a friend asks you to do the following:

(a) choose any number from 0 to 10.
(b) divide the number by \\(-2\\).
(c) add 8 to the result.

draw a graph to represent the relationship between the number selected and the result. let \\(x\\) represent the number selected and let \\(y\\) represent the result.

Explanation:

Translate the verbal instructions into an algebraic equation

$$ y = \frac{x}{-2} + 8 = -\frac{1}{2}x + 8 $$

Determine the domain and range based on the constraints

$$
LATEXBLOCK0
$$

Identify key points for graphing the line segment

$$
LATEXBLOCK1
$$

Answer:

The relationship between the selected number \(x\) and the result \(y\) is represented by the linear equation:

$$ y = -\frac{1}{2}x + 8 \quad \text{for } 0 \le x \le 10 $$

The graph is a line segment starting at the point \((0, 8)\) and ending at the point \((10, 3)\).