Chapter 1.5, Problem 43PPS

(a)

To determine

To state: whether the resulting statement is true or false.

Explanation of Solution

Given information:

Organize the following into a table.

Substitute 5 points into the inequality $y\ge -\frac{1}{2}x+3$ .

Calculation:

Now, construct a table for each statement.

	$\left(0,0\right)$	$\left(1,1\right)$	$\left(2,2\right)$	$\left(3,3\right)$	$\left(4,4\right)$
$y\ge -\frac{1}{2}x+3$	$0\ge 3$	$1\ge \frac{5}{2}$	$2\ge 2$	$3\ge \frac{3}{2}$	$4\ge 1$
	False	False	True	True	True

(b)

To determine

To sketch: the graph of the given equation and to graph the 5 points from the table.

Explanation of Solution

Given information:

Given equation is

  $y=-\frac{1}{2}x+3$

Calculation:

The graph are shown below,

(c)

To determine

To describe: the pattern produced by the point labeled, to make a conjecture about which points on the coordinate plane would result in true and false statements.

Explanation of Solution

Calculation:

All the points below the line are False and all the points above or on the line are True.

Points on the line are also considered true since the inequality is greater or equal to.