seconds.
Speed of an African Tiger Beetle
Time, x (seconds) Distance, y (meters)
5 12.5
10 25.0
15 37.5
20 50.0
25 62.5
Based on information in the table, which equation can be used to model the relationship between x and y?
The relationship between x (time in seconds) and y (distance in meters) in the table is a linear relationship. The distance increases by a constant rate of 12.5 meters every 5 seconds.
Therefore, the equation that can be used to model this relationship is:
y = 2.5x
To find the equation that models the relationship between x (time in seconds) and y (distance in meters), we need to determine the pattern in the data. Let's first calculate the velocity or speed for each time interval:
Velocity = Distance / Time
For the given data, we can calculate the velocity as follows:
Velocity at 5 seconds = 12.5 meters / 5 seconds = 2.5 meters/second
Velocity at 10 seconds = 25.0 meters / 10 seconds = 2.5 meters/second
Velocity at 15 seconds = 37.5 meters / 15 seconds = 2.5 meters/second
Velocity at 20 seconds = 50.0 meters / 20 seconds = 2.5 meters/second
Velocity at 25 seconds = 62.5 meters / 25 seconds = 2.5 meters/second
From the calculations, it is evident that the velocity remains constant at 2.5 meters/second for each time interval. This suggests that the relationship between x (time) and y (distance) is a linear one.
The equation that represents a linear relationship is given by:
y = mx + b
where m is the slope and b is the y-intercept.
To find the equation, we need to determine the slope and y-intercept. Since the velocity is constant at 2.5 meters/second, the slope (m) will be 2.5.
Next, let's look at the table to find the y-intercept. At 5 seconds, the distance is 12.5 meters. This means that when x = 0, y = 12.5. Therefore, the y-intercept (b) is 12.5.
Putting it all together, the equation that models the relationship between x and y is:
y = 2.5x + 12.5
To determine the equation that models the relationship between the time (x) and distance (y) for an African Tiger Beetle, we need to analyze the given data.
Looking at the table, we can observe that for every 5-second increment, the distance covered by the beetle increases by 12.5 meters. This indicates that the relationship between x and y is linear.
To find the equation, we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
First, let's calculate the slope (m):
m = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)
Let's take the first and second data points (5, 12.5) and (10, 25.0):
m = (25.0 - 12.5) / (10 - 5) = 12.5 / 5 = 2.5
Now that we have the slope, let's find the y-intercept (b). We can choose any point in the table to substitute into the equation to solve for b. Let's use the point (5, 12.5):
y = mx + b
12.5 = 2.5 * 5 + b
12.5 = 12.5 + b
b = 12.5 - 12.5
b = 0
Therefore, the equation that models the relationship between x and y is:
y = 2.5x
In this equation, x represents time in seconds, and y represents distance covered in meters by the African Tiger Beetle.