Chapter 1.6, Problem 33IP

Solution

(a)

To make the table of ordered pairs in which x-coordinate represents the number hours and y-coordinate represents the number of miles hiked in 1,2,4,and 6 hours.

x(Number of hours)	y(miles hiked)	(x,y)
1	$3\times 1=3$	(1,3)
2	$3\times 2=6$	(2,6)
4	$3\times 4=12$	(4,12)
6	$3\times 6=18$	(6,18)

GIVEN:

Aarona is hiking in a state park. He averages 3 miles per hour.

Concept Used:

In rectangular coordinate system any poin be in the form of $\left(x,y\right)$ .

• In Quadrant I, both the coordinates of ordered pair are positive, that is, $\left(+,+\right)$ .
• In Quadrant II, first number is negative and second is positive, that is, $\left(-,+\right)$ .
• In Quadrant III, both the coordinates of ordered pair are negative, that is, $\left(-,-\right)$ .
• In Quadrant IV, first point is positive and second is negative, that is, $\left(+,-\right)$ .

Explanation:

To make the table of ordered pairs in which x-coordinate represents the number hours and y-coordinate represents the number of miles hiked in 1,2,4,and 6 hours.

The table is:

x(Number of hours)	y(miles hiked)	(x,y)
1	$3\times 1=3$	(1,3)
2	$3\times 2=6$	(2,6)
4	$3\times 4=12$	(4,12)
6	$3\times 6=18$	(6,18)

(b)

To plot the graph of ordered pairs.

  

GIVEN:

Aarona is hiking in a state park. He averages 3 miles per hour.

Concept Used:

In rectangular coordinate system any poin be in the form of $\left(x,y\right)$ .

• In Quadrant I, both the coordinates of ordered pair are positive, that is, $\left(+,+\right)$ .
• In Quadrant II, first number is negative and second is positive, that is, $\left(-,+\right)$ .
• In Quadrant III, both the coordinates of ordered pair are negative, that is, $\left(-,-\right)$ .
• In Quadrant IV, first point is positive and second is negative, that is, $\left(+,-\right)$ .

Explanation: In order to plot the point $\left(1,3\right)$ , observe that both numbers of the ordered pair are positive, so the point will be in first quadrant.To plot the graph of the point, first move 1 units to the right starting from origin and then move 3 units up.

In order to plot the point $\left(2,6\right)$ , observe that both numbers of the ordered pair are positive, so the point will be in first quadrant.To plot the graph of the point, first move 2 units to the right starting from origin and then move 6 units up.

In order to plot the point $\left(4,12\right)$ , observe that both numbers of the ordered pair are positive, so the point will be in first quadrant.To plot the graph of the point, first move 4 units to the right starting from origin and then move 12 units up.

In order to plot the point $\left(6,18\right)$ , observe that both numbers of the ordered pair are positive, so the point will be in first quadrant.To plot the graph of the point, first move 6 units to the right starting from origin and then move 18 units up

The graph of the point is shown below: