Given the table for x, time in minutes and y, distance traveled:
x - time 4 3 10 7 9
y - distance 76 57 190 133 171
a. Every minute _ meters are traveled.
b. Write an equation to show the relationship between x and y. _
c. This relationship is _ because the y-intercept is _
The word bank:
(0,0) , 76 , (0,57) , y=x-19 , y=133x , 19 , non proportional , 57 , y=19x , proportional , y=x/19 , (4,79) , 19y=x , (0, 19) , -19 , 133
a. Every minute, 19 meters are traveled.
b. The equation to show the relationship between x and y is y = 19x.
c. This relationship is proportional because the y-intercept is (0,0).
To answer these questions, we need to analyze the given table:
x - time: 4, 3, 10, 7, 9
y - distance: 76, 57, 190, 133, 171
a. To find out how many meters are traveled every minute, we can calculate the difference in distance between consecutive time intervals:
- Between 4 and 3 minutes: 76 - 57 = 19 meters
- Between 3 and 10 minutes: 57 - 190 = -133 meters
- Between 10 and 7 minutes: 190 - 133 = 57 meters
- Between 7 and 9 minutes: 133 - 171 = -38 meters
The distances traveled are not consistent for each minute, so we cannot determine a fixed value for "meters traveled every minute." Instead, the distances vary.
b. To write an equation showing the relationship between x and y, we can examine the table for any patterns.
One possible equation is: y = 19x. This equation suggests that every minute, 19 meters are traveled. However, since the distances in the table are not consistent, this equation does not accurately represent the relationship.
Another possible equation is: y = x - 19. This equation suggests that the distance traveled is the time minus 19. While it does not perfectly match all the values in the table, it is a closer representation than the previous equation.
c. Based on the equation y = x - 19, the relationship between x and y can be described as non-proportional because the coefficient of x (-19) is not a constant value.
Additionally, if we consider the y-intercept (the point where x = 0), the equation becomes y = 0 - 19, which simplifies to y = -19. This implies that when no time has passed (x = 0), the distance traveled is -19. Therefore, the relationship is non-proportional, and the y-intercept is -19.
a. Every minute 19 meters are traveled.
b. The equation to show the relationship between x and y is y = 19x.
c. This relationship is proportional because the y-intercept is (0,0).