Given the table for x, time in minutes and y, distance traveled in meters:
X-time(minutes) 8,5,7,2,9
y-distance(meters) 40,25,35,10,45,
A. every minute is [enter answer] meters traveled
B. write an equation to show the relationship between x and y.
C, the relationship is [enter answer] because the y intercept is [enter answer]
A. To find how many meters are traveled per minute, we can calculate the difference in distance divided by the difference in time for each pair of values.
For the first pair (8 minutes, 40 meters) and the fourth pair (2 minutes, 10 meters), the difference in distance is 40 - 10 = 30 meters, and the difference in time is 8 - 2 = 6 minutes. Therefore, the rate of meters traveled per minute is 30 / 6 = 5 meters traveled per minute.
For the second pair (5 minutes, 25 meters) and the third pair (7 minutes, 35 meters), the difference in distance is 35 - 25 = 10 meters, and the difference in time is 7 - 5 = 2 minutes. So, the rate of meters traveled per minute is 10 / 2 = 5 meters traveled per minute.
For the last pair (9 minutes, 45 meters), we cannot determine the rate of meters traveled per minute since there are no subsequent pairs to compare it to.
Therefore, the answer is that every minute, 5 meters are traveled.
B. To write an equation to show the relationship between x and y, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope (rate of change) and b is the y-intercept.
We already found that the rate of meters traveled per minute is 5. Now, let's find the y-intercept. From the given data, we can see that when x = 0, y is 0. However, there is no data point where x = 0. We can estimate the y-intercept by finding the equation of the line that passes through two of the given points. Let's use the first and last points: (8, 40) and (9, 45).
First, find the slope (m): m = (45 - 40) / (9 - 8) = 5 / 1 = 5
Now, substitute the slope and one of the points (8, 40) into the equation y = mx + b to solve for b: 40 = 5(8) + b
40 = 40 + b
b = 40 - 40
b = 0
So, the equation to show the relationship between x and y is y = 5x.
C. The relationship between x and y is a direct variation because the equation can be written in the form y = kx, where k is the constant of variation. In this case, k is 5. The y-intercept is 0, indicating that the line passes through the origin.
is C. proportional, non proportional or non linear
I apologize for the incorrect response in the previous answer.
C. The relationship between x and y is non-proportional because the equation is y = 5x, not y = kx where k is a constant. In a proportional relationship, the equation would have the form y = kx, where k is the constant of proportionality. In this case, the equation is linear, but not proportional since the y-intercept is 0, indicating that the line passes through the origin.
A. To find out how many meters are traveled every minute, we can calculate the difference in distance for consecutive minutes.
For example, for the first two minutes (x=5 and x=8), the distance traveled is 25 meters and 40 meters respectively. The difference is 40 - 25 = 15 meters.
So, every minute, 15 meters are traveled.
B. To write an equation showing the relationship between x and y, we can use the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
Let's calculate the slope first:
Slope (m) = (change in y) / (change in x)
For the given data, let's consider the first and last points (8,40) and (9,45).
(change in y) = 45 - 40 = 5
(change in x) = 9 - 8 = 1
Slope (m) = 5/1 = 5
Now let's find the y-intercept (b) using the formula: b = y - mx
Considering any point, (x,y) from the given data, we can substitute the values:
Using point (2,10):
10 = (5)(2) + b
10 = 10 + b
b = 10 - 10
b = 0
So the equation relating x and y is:
y = 5x
C. The relationship is "linear" because the equation we found, y = 5x, is a linear equation since the highest power of x is 1.
The y-intercept is 0, which means that when x is 0, the distance traveled is also 0. In this case, it means that at the starting point (x=0), no distance has been covered yet.
To answer these questions, we can examine the given table for x (time in minutes) and y (distance traveled in meters):
X-time (minutes): 8, 5, 7, 2, 9
Y-distance (meters): 40, 25, 35, 10, 45
A. To find out how many meters are traveled every minute, we can calculate the difference in distance divided by the difference in time. Let's take the first two data points as an example: (8, 40) and (5, 25). The difference in distance is 40 - 25 = 15 meters, and the difference in time is 8 - 5 = 3 minutes. So, the distance traveled every minute is 15 meters / 3 minutes = 5 meters. Therefore, every minute, we travel 5 meters.
B. To write an equation that shows the relationship between x (time) and y (distance), we can analyze the pattern in the given data. Let's observe the table and examine how x and y values change:
X | Y
--------
8 | 40
5 | 25
7 | 35
2 | 10
9 | 45
Based on the data, it seems that the distance traveled (y) is related to the time (x) through a linear equation. We can use the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
To find the slope (m), we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Let's choose two data points to calculate the slope, for example, (5, 25) and (8, 40):
m = (40 - 25) / (8 - 5)
m = 15 / 3
m = 5
Now that we have the slope, we can substitute it into the equation: y = 5x + b.
To find the y-intercept (b), we can choose any point from the table. Let's use (5, 25):
25 = 5(5) + b
25 = 25 + b
b = 0
Therefore, the equation that shows the relationship between x and y is y = 5x.
C. Based on the equation y = 5x, the relationship between x (time) and y (distance) can be described as a proportional relationship because the equation is in the form of y = mx, where m is the constant ratio. The y-intercept is 0, which means that when the time is 0, the distance traveled is also 0.