Question

A car travels at a constant speed. The table below shows the distance traveled over time. Graph the proportional relationship.


Time (hours) Distance (miles)
1 60
2 120
3 180


a)A straight line passing through the origin with a slope of 60.
b)A straight line passing through the origin with a slope of 30.
c)A curved line passing through the origin.

Answer 1

To graph the proportional relationship from the data provided in the table, we first examine the relationship between time and distance.

The table shows:

- At 1 hour, the distance is 60 miles.
- At 2 hours, the distance is 120 miles.
- At 3 hours, the distance is 180 miles.

To determine the slope of the line, we can calculate the distance per unit of time:

- The distance traveled in 1 hour is 60 miles.
- The distance traveled in 2 hours is 120 miles, which is \(120 \text{ miles} / 2 \text{ hours} = 60 \text{ miles/hour}\).
- The distance traveled in 3 hours is 180 miles, which is \(180 \text{ miles} / 3 \text{ hours} = 60 \text{ miles/hour}\).

This indicates that the relationship is linear and proportional, where the distance traveled increases consistently by 60 miles for each hour.

The graph of this relationship will be a straight line passing through the origin (0,0) with a slope of 60, meaning for every hour, it goes up 60 on the y-axis (distance).

Therefore, the correct answer is:

**a) A straight line passing through the origin with a slope of 60.**