Greg rode his bicycle at a constant speed of 20 miles per hour. Plot points on the graph to present the distances Greg rode after 1,2,3, and 4 hours (1 hour = 20 miles, 2 hours = 40, 3 hours = 60, 4 hours = 80 miles). Write an equation to represent the relationship between distance, d, and time, t.
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Ok, but what is is the equation?
To plot the points on the graph, we can create a table to represent the relationship between distance and time:
Time (hours) | Distance (miles)
-------------------------
1 | 20
2 | 40
3 | 60
4 | 80
Now, let's plot these points on a graph:
(1, 20)
(2, 40)
(3, 60)
(4, 80)
To write an equation to represent the relationship between distance, d, and time, t, we can use the formula:
d = r * t
Where:
d is the distance,
r is the constant speed (20 miles per hour),
and t is the time.
So, the equation representing the relationship between distance and time is:
d = 20 * t
To plot points on the graph representing the distance Greg rode after certain hours, we can create a table with two columns: time (t in hours) and distance (d in miles).
| Time (t) | Distance (d) |
|----------|--------------|
| 1 | 20 |
| 2 | 40 |
| 3 | 60 |
| 4 | 80 |
With these points, we can now plot them on a graph. The x-axis represents time (t), and the y-axis represents distance (d). Each point would be plotted at the corresponding time and distance. Once we have all the points plotted, we can connect them to make a line.
Now, to find the equation representing the relationship between distance (d) and time (t):
Since Greg is riding his bicycle at a constant speed of 20 miles per hour, the relationship is linear. This means that the distance Greg rode is directly proportional to the time he has ridden.
We can use the equation of a straight line, which is y = mx + b, where:
- y represents the dependent variable (distance in this case),
- x represents the independent variable (time in this case),
- m represents the slope of the line,
- b represents the y-intercept.
In our case, the slope (m) represents the rate at which the distance is changing with respect to time, which is the speed of 20 miles per hour. And the y-intercept (b) represents the distance at which Greg started riding, which is 0 miles (since he starts at the initial position).
Therefore, the equation representing the relationship between distance (d) and time (t) is: d = 20t.
This equation shows that for every hour Greg rides, the distance he covers can be calculated by multiplying 20 (the speed) by the time in hours (t).