Question

practice

1. the cross country team practices by jogging on the town’s streets. the average jogging rate is 6 miles per hour. one member jogged for 3.5 hours one weekend. how many miles did the team member jog?

a. complete the table to relate the number of miles to the number of hours jogged.

x	y
1
2
3

b. graph the ordered pairs on the coordinate plane.
(coordinate plane with x-axis 0 - 6 and y-axis 0 - 20)
c. write an equation that describes the relationship. then solve the problem.

Explanation:

Part a: Complete the Table

Step 1: Recall the formula for distance

The formula for distance \( d \) is \( d = r \times t \), where \( r \) is the rate (speed) and \( t \) is the time. Here, the rate \( r = 6 \) miles per hour. For each time \( x \) (in hours), the distance \( y \) (in miles) is \( y = 6x \).

Step 2: Calculate for \( x = 1 \)

Substitute \( x = 1 \) into \( y = 6x \): \( y = 6 \times 1 = 6 \).

Step 3: Calculate for \( x = 2 \)

Substitute \( x = 2 \) into \( y = 6x \): \( y = 6 \times 2 = 12 \).

Step 4: Calculate for \( x = 3 \)

Substitute \( x = 3 \) into \( y = 6x \): \( y = 6 \times 3 = 18 \).

So the table becomes:

\( x \)	\( y \)
2	12
3	18

Part b: Graph the ordered pairs

Step 1: Identify the ordered pairs

From the table, the ordered pairs are \( (1, 6) \), \( (2, 12) \), and \( (3, 18) \).

Step 2: Plot the points on the coordinate plane

• For \( (1, 6) \): Move 1 unit to the right on the \( x \)-axis and 6 units up on the \( y \)-axis.
• For \( (2, 12) \): Move 2 units to the right on the \( x \)-axis and 12 units up on the \( y \)-axis.
• For \( (3, 18) \): Move 3 units to the right on the \( x \)-axis and 18 units up on the \( y \)-axis.

(Note: Since the graph is not fully visible in terms of grid size, but following the scale, these points should lie on a straight line with a slope of 6.)

Part c: Write the equation and solve the problem

Step 1: Write the equation

From the relationship \( y = 6x \), where \( x \) is the time in hours and \( y \) is the distance in miles.

Step 2: Solve for \( x = 3.5 \) hours

Substitute \( x = 3.5 \) into the equation \( y = 6x \):
\( y = 6 \times 3.5 = 21 \).

Answer:

Part a:

The completed table is:

\( x \)	\( y \)
2	12
3	18

Part b:

The ordered pairs \( (1, 6) \), \( (2, 12) \), and \( (3, 18) \) are plotted on the coordinate plane (as described in the steps).

Part c:

The equation is \( y = 6x \). The team member jogged \( \boldsymbol{21} \) miles.