Question

x f(x) 100 60 24 45 18 30 12 Some values of the linear function f are given in the table shown. What is the value of f(100)? A. 30 B. 36 C. 40 D. 48

Answer 1

The value of f(100) is 40

The equation for a linear function is written in the form ;

• y = bx + c
• c = intercept; b = slope

Using the pair of points to find the slope

(45, 18) ; (30, 12)

Slope = change in y / change in x

• Change in y = 12 - 18 = -6
• Change in x = 30 - 45 = -15

Slope = -6/-15 = 0.4

Now ;

• y = 0.4x + c

Using the pair (30, 12) to find c

12 = 0.4(30) + c

12 = 12 + c

c = 12 - 12

c = 0

Hence, the linear function is y = 0.4x

To obtain f(100)

substitute x = 100 into the equation

y = 0.4(100)

y = 40

Therefore, f(100) is 40