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13. Selected values of a linear function f(x) are given in the table below. Find the value of k. Show/explain how you arrived at your answer. t - 8 -33 4 - 2 - 12 12 k 14 44 18 58 i U Font Family AA- O o = = = it

13 Selected values of a linear function fx are given in the table below Find the value of k Showexplain how you arrived at your answer t 8 33 4 2 12 12 k 14 44 class=

Respuesta :

-8........-33

-2........-12

4..........9

12........k

14.......44

18.......58

The equation of a line is: y = mx + b

where m is the slope and b is the y interception

m = (y2 - y1)/(x2 - x1)

if we use the first two points: m = (-12 + 33)/(-2 + 8) = 21/6.... m= 21/6

so the equation of the line is y = (21/6)x + b

to find the value of, we use the third point:

y = (21/6)x + b

9 = (21/6)(4) + b = 84/6 + b = 14 + b

9 - 14 = b

b = -5

the equation ot the line is y = (21/6)x - 5

when x = 12

y = (21/6(12) - 5 = 42 - 5 = 37

so, when the first value is 12, k = 37

The anser is 37