The table shows the number of miles driven over time. Find the rate of change.

x- y-
4 | 204
6 | 306
8 | 408
10 | 510

A.) 51/1; Your car travels 51 miles every 1 hour. *
B.) 204; Car travels 204 miles
C.) 1/51; Car travels 51 miles every 1 hour. *

The wording on A and C is confusing me.

But... Which one would it be?? They both have 51 miles every hour?

204/4 = 51

51mph...
So would it be 51/1?

Yes, Yes, Yes.

I'm pretty sure it's 51 but idk if it's A or C

It's miles per hour.

Which would mean miles per hour, 51/1 or 1/51?

51/1?

This would be clearer if you had labeled the table

hr- mi-
4 | 204
6 | 306
8 | 408
10 | 510

Then it would be clear that to get mi/hr you divide the number in the "mi" column by that in the "hr" column.

To find the rate of change, we need to look at the change in the y-values (miles driven) for each unit change in the x-values (time).

Let's calculate the differences between consecutive y-values for the given x-values:

Difference between 306 and 204: 306 - 204 = 102
Difference between 408 and 306: 408 - 306 = 102
Difference between 510 and 408: 510 - 408 = 102

As we can see, the differences are consistent. This means that for every 2-unit increase in x (change from 4 to 6, 6 to 8, and 8 to 10), the y-value increases by 102.

Now, let's consider the options provided:

A.) 51/1; Your car travels 51 miles every 1 hour.
B.) 204; Car travels 204 miles.
C.) 1/51; Car travels 51 miles every 1 hour.

Option A implies that the car travels 51 miles for every 1-hour, but that is not consistent with the data in the table. The differences between consecutive y-values are not equal to 51.

Option B states that the car travels 204 miles, which is not correct because the mileage increases by 102 for each 2-unit increase in x.

Option C suggests that the car travels 51 miles every 1 hour. This option is consistent with the differences between consecutive y-values, as we found earlier (102 for each 2-unit increase in x).

Therefore, the correct option is C.) 1/51; Car travels 51 miles every 1 hour. The rate of change is 51 miles per hour.