Question

Write a linear function f with f(-3)=1 and f(13)=5.

Answer 1

0.25x+1.75

Explanation:

A linear equation is of the form ax+b. Set a up a system of equation with -3 and 13 substituted in to ax+b. We get -3a+b=1 and 13a+b=5. Solving tis gives us a,b=(0.25,1.75)

Answer 2

f(x) =
`(1)/(4)` x +
`(7)/(4)`

Explanation:

a linear function has the form

f(x) = ax + b ( a and b have to be found )

given f(- 3) = 1 and f(13) = 5 , then by substitution

- 3a + b = 1 → (1)

13a + b = 5 → (2)

subtract (2) from (1) term by term to eliminate b

- 3a - 13a = 1 - 5

- 16a = - 4 ( divide both sides by - 16 )

a =
`(-4)/(-16)` =
`(1)/(4)`

substitute a =
`(1)/(4)` into (1) and solve for b

- 3(
`(1)/(4)` ) + b = 1

-
`(3)/(4)` + b = 1 ( add
`(3)/(4)` to both sides )

b = 1
`(3)/(4)` =
`(7)/(4)`

f(x) =
`(1)/(4)` x +
`(7)/(4)` ← is the linear function

or

f(x) = 0.25x + 1.75