Question

4. Given the table for x, time in minutes, and y, distance traveled:

x: time 8 5 7 2 9
y: distance 664 415 581 166 747


(4 points)
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
.

Answer 1

a. To find the rate at which meters are traveled per minute, we can calculate the average distance traveled per minute. The total distance traveled is:

664 + 415 + 581 + 166 + 747 = 2,573

The total time taken is:

8 + 5 + 7 + 2 + 9 = 31

Therefore, the average distance traveled per minute is:

2,573 / 31 ≈ 83.06

So, approximately 83 meters are traveled every minute.

b. To write an equation to show the relationship between x (time) and y (distance), we can use a linear equation in the form y = mx + c, where m is the slope and c is the y-intercept.

We can find the slope by finding the change in y divided by the change in x. Taking two points, let's say (8, 664) and (2, 166), the change in y is:

664 - 166 = 498

And the change in x is:

8 - 2 = 6

So, the slope is:

m = 498 / 6 = 83

Therefore, the equation is:

y = 83x + c

To find the value of c, we can substitute any of the given points into the equation. Let's use the point (8, 664):

664 = 83(8) + c

Simplifying:

664 = 664 + c

c = 0

So, the equation is:

y = 83x

c. This relationship is linear because the equation is in the form of a linear equation: y = 83x. The y-intercept is 0.