Question

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

Answer 1

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

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