Which graph represents a bike traveling at a constant rate of 12 miles per hour
The Correct Answer and Explanation is:
✅ Correct Answer:
A straight line graph that starts at the origin (0,0) and has a constant positive slope represents a bike traveling at a constant rate. The slope of the line should be 12, since the bike is traveling 12 miles for every hour.
📈 Explanation
To determine which graph shows a bike traveling at a constant rate of 12 miles per hour, let’s recall what a distance-time graph looks like for constant speed.
In such a graph:
- The horizontal axis (x-axis) represents time (in hours),
- The vertical axis (y-axis) represents distance (in miles).
A constant speed means that for every unit of time, the same amount of distance is covered. This is shown on a graph as a straight line because the rate of change (slope) doesn’t vary. The formula to represent this relationship is:Distance=Rate×Time\text{Distance} = \text{Rate} \times \text{Time}Distance=Rate×Time
Given the rate is 12 miles per hour, the equation becomes:y=12xy = 12xy=12x
This is a linear equation with:
- A slope of 12,
- A y-intercept of 0 (since at time 0, the distance is also 0).
So, every hour, the distance increases by 12 miles:
- At 1 hour: 12 miles
- At 2 hours: 24 miles
- At 3 hours: 36 miles
- And so on…
Any graph that shows a straight line through the origin with these points plotted will correctly represent a constant speed of 12 mph.
Common wrong answers may include:
- A curved line (suggests changing speed),
- A flat line (suggests no movement),
- A line that doesn’t pass through the origin (implies starting with distance, not realistic for this context).
Therefore, the correct graph is a straight line through the origin with a slope of 12.
