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)
a. Every minute 40 meters are traveled.
b. Write an equation to show the relationship between x and y.
y = 40x
c. The relationship is proportional because the y-intercept is 0.
a. Every minute, 5 meters are traveled.
b. The equation for the relationship between x and y is y = 5x.
c. The relationship is proportional because the y-intercept is 0.
To answer this question, we need to analyze the given table for x and y. Here is how you can determine the correct responses:
a. To find the rate of distance traveled per minute, we can look at the values in the y column (distance in meters) and observe the changes when the x column (time in minutes) increases by 1 each time. By comparing the values, we can see that for every minute, 5 meters are traveled. Therefore, the correct response for this question is "Every minute 5 meters are traveled."
b. To write an equation showing the relationship between x (time) and y (distance), we need to identify the pattern. Looking at the table, we can see that when x increases by 1, y increases by 5. This suggests a proportional relationship between x and y. The equation for a proportional relationship is y = kx, where k is the constant of proportionality. In this case, since y increases by 5 each time x increases by 1, k = 5. Therefore, the correct equation is "y = 5x."
c. To determine the relationship type based on the y-intercept, we need to check the y value when x is equal to 0. From the table, when x = 0, y = 25. Since the y-intercept is not zero, the relationship is not linear. However, since the y-intercept is a positive value, we can conclude that it is a non-linear proportional relationship. Therefore, the correct response is "The relationship is non-linear because the y-intercept is 25."
Based on the above explanations, the correct responses are:
a. Every minute 5 meters are traveled.
b. y = 5x.
c. The relationship is non-linear because the y-intercept is 25.