You are trying twice a week for a race on Monday you go 4 miles and 40 minutes then on Wednesday you go 2 miles in 16 minutes right and equation where y is the number of miles and s is the time and minutes for the day you ran the fastest for the week
To find the equation representing the relationship between the number of miles (y) and the time in minutes (s) for the day you ran the fastest in a week, we need to compare the two given data points.
Firstly, let's determine which day you ran the fastest. From the given information, we know that you ran 4 miles in 40 minutes on Monday and 2 miles in 16 minutes on Wednesday. Since the time is faster on Wednesday, this day represents the fastest run of the week.
Now, let's create the equation. We can use the equation of a line in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
We need to find the values of m and b. The slope (m) represents the rate at which you ran (miles per minute), and the y-intercept (b) represents the distance you would run without any time passing (y when s = 0).
Using the two data points, we can calculate the slope (m):
m = (change in y) / (change in s)
m = (2 - 0) / (16 - 0)
m = 2/16
m = 1/8
Now, we can plug in the values of m and one of the data points (2 miles, 16 minutes) into the slope-intercept form equation and solve for b:
2 = (1/8)(16) + b
2 = 2 + b
b = 2 - 2
b = 0
Therefore, the equation representing the relationship between the number of miles (y) and the time in minutes (s) for the day you ran the fastest in a week is:
y = (1/8)s