2. Given the table for x, time in minutes and y, distance traveled in meters:%0D%0A%0D%0Ax - time (minutes)%098%095%097%092%099%0D%0Ay - distance (meters)%0940%0925%0935%0910%0945%0D%0A %0D%0A%0D%0A(4 points)%0D%0APut responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.%0D%0Aa. Every minute Response area meters are traveled.%0D%0A%0D%0Ab. Write an equation to show the relationship between x and y. Response area %0D%0A%0D%0Ac. The relationship is Response area because the y-intercept is Response area%0D%0A%0D%0Aproportionalnon proportionalnon linear-5540-40y = x/55y = xy = x - 5y = 5xy = 40x40y = x(5, 25)(0, 5)(0, 0)(5, 0)%0D%0AQuestion 3%0D%0A3. 
a. Every minute 35 meters are traveled.
b. Write an equation to show the relationship between x and y.
The equation is y = 5x.
c. The relationship is proportional because the y-intercept is 0.
a. Every minute 10 meters are traveled.
b. The equation to show the relationship between x and y is: y = 10x.
c. The relationship is proportional because the y-intercept is 0.
To answer the given question, let's analyze the information provided:
Given table:
x - time (minutes): 8, 5, 7, 2, 9
y - distance (meters): 40, 25, 35, 10, 45
a. To determine how many meters are traveled every minute, we can calculate the average speed. We divide the change in distance by the change in time for any two points.
For example, let's consider the first two points (8 minutes, 40 meters) and (5 minutes, 25 meters):
Average speed = (40 - 25) meters / (8 - 5) minutes = 15 meters / 3 minutes = 5 meters per minute
Therefore, the correct response for (a) is "Every minute 5 meters are traveled."
b. To write an equation to show the relationship between x and y, we need to identify how x and y are related based on the given data. Since we are looking for a linear relationship, we can use the formula for a straight line:
y = mx + b
To find the values of m and b, we can use any two points from the given data. Let's use points (8, 40) and (5, 25):
m = (y2 - y1) / (x2 - x1) = (25 - 40) / (5 - 8) = -15 / -3 = 5
Using the point (8, 40):
40 = 5 * 8 + b
40 = 40 + b
b = 0
Therefore, the equation that represents the relationship between x and y is: y = 5x.
The correct response for (b) is "y = 5x".
c. To determine the nature of the relationship (proportional, non-proportional, or non-linear) based on the y-intercept, we can analyze the value of b in the equation.
If b is 0, then the relationship is proportional.
If b is not 0, then the relationship is non-proportional.
If the relationship cannot be represented by a straight line, then it is non-linear.
In the equation y = 5x, the y-intercept (b) is 0. Therefore, the relationship is proportional.
The correct response for (c) is "proportional".
I hope this explanation helps you understand how to find the answers to the given questions.