Write a linear function f with the values f (2) = 4 and f (-7) = 9. A function is f (x) =

f (x) = - 5/9 x + 5 1/9

Step-by-step explanation:

f (2) = 4 and f (-7) = 9 means the line pass through (2,4) and ( - 7,9)

f (x) = mx + b

m = (y-y') / (x-x') = (9 - 4) / ( - 7 - 2) = - 5/9

for (2,4) : b = f (x) - mx = y - mx = 4 - ( - 5/9) x 2 = 4 + 10/9 = 46/9 = 5 1/9

f (x) = - 5/9 x + 5 1/9

check for (-7, 9) f (-7) = (-5/9) * (-7) + 5 1/9 = 35/9 + 46/9 = 81/9 = 9