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:

Formulate the linear equation

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

Determine key boundary points

$$
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$$

Plot the line segment

$$ \text{Segment connecting } (0, 8) \text{ and } (10, 3) $$

Answer:

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

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

with the domain restriction \(0 \le x \le 10\).

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