The table represents a linear function. Find the values of a, b, and c. Show your work.

x | y

a 7

3 8

5 9

7 b

c 11

mx+n=y

m*3+n=8

m*5+n=9

=>m*5+n - (m*3+n) = 9-8

2m=1 = > m=1/2

½ * 3 + n = 8

n=8-3/2

n=13/2

=> y=x/2 + 13/2

y = (x+13) / 2

7 = (a+13) / 2; a+13=14 = > a=1

b = (7+13) / 2; b=20/2; b=10

11 = (c+13) / 2, c+13=22 = > c=9

a = 1, b = 10, c = 9

Step-by-step explanation:

x is increasing by positive two from each number and y is increasing by 1 from each number.