if a linear function f satisfies the conditions: f(-3)=-4 and f(3)=14 find f(x)

Answer 1

Recap what is a linear function : f(x) = ax + b , where a and b are constant coefficients with a≠0

Apply the given condtions:

f(-3) = -4 => -3a + b = -4 .... (i)

f(3) = 14 => 3a + b = 14 ..(ii)

Subtract (ii) from( i)

-6a = -18 =>a=3

From (ii) b = 14 -3a = 14 -3(3) = 5

f(x) = 3x + 5 [Ans]

Verify by plugging in the given values.

Answer 2

(-3,-4) and (3,14) are two points on the line, having slope = 18/6 = 3

y=3x + b

-4 = 3(-3) + b

b = 5

y=3x+5

f(x) = 3x+5