Question

If f(x) is a linear function ,f(-1)=-3 , and f(4)=-5 , find an equation for f(x)

Answer 1

Answer:

        f(x) = -²/₅ x - ¹⁷/₅

Step-by-step explanation:

The equation of the linear function: f(x) = mx + b

f(-1) = -3   ⇒   -3 = m(-1) + b  ⇒   m = b + 3

f(4)=-5   ⇒   -5 = m×4 + b  

                   -5 = 4(b+3) + b

                   -5 = 4b + 12 + b

                    5b = -5 - 12

                      b = -¹⁷/₅

m = -¹⁷/₅ + 3 = -¹⁷/₅ + ¹⁵/₅ = -²/₅

Therefore the function:

                                    f(x) = -²/₅ x - ¹⁷/₅