Write an equation: At 2 claps, Joe is in position 7 and walking towards zero at a rate of 3 claps per minute.

I'll assume "position 7" refers to distance and not to the order of other people.  

Step-by-step explanation:

We want an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).  We can assume that "claps" is a new measure of distance.  0 claps is the finish.

Let's express the information provided in point format.

"At 2 claps, Joe is in position 7"  is (2,7)  2 is the distance (claps) and 7 is the time (minutes)

And we can say the rate is also the slope of a line.  "rate of 3 claps per minute" is 3c/m, where c is claps and m is minutes.

We can start a line equation by stating y = 3x + b, where we're using the rate, 3 c/m, as the slope, m.

We need to determine the value of b.  We can use the given point (2,7) and solve for m:

y = 3x + b

7 = 3*(2) + b

b = 1

The equation becomes y = 3x + 1

y is the distance in claps and x is the time in minutes.

At a time of 2 claps he is at position of 7.  b = 1 means he started 1 clap further from the finish at 0 claps.

To find the time required to reach the finish, we need to know the total distance, in claps.

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step-by-step explanation: