Jin is tracking how much food he feeds his dog each week. After 2 weeks, he has used 8 1/2 cups of dog food. After 5 weeks, he has used 21 1/4 cups. Construct a function in the form y=mx+b to represent the amount of dog used ,y, after x weeks

y = 4.25x

Step-by-step explanation:

The function that we want to construct is a linear function:

y=mx+b

To find the values of the parameters m and b, we just need to use the two points that the question gave:

in two weeks, he used 8 1/2 = 8.5 cups, so for x = 2 we have y = 8.5.

in five weeks, he used 21 1/4 = 21.25 cups, so for x = 5 we have y = 21.25.

Then, we apply these values in the equation:

8.5 = 2m + b

21.25 = 5m + b

Subtracting the first equation from the second, we have:

3m = 12.75

m = 4.25

Now we use the value of m in the first equation to find the value of b:

8.5 = 2*4.25 + b

8.5 = 8.5 + b

b = 0

So, our equation will be y = 4.25x

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.