Question

F(0) = -5, f(4) = -3

Answer 1

y =
`(1)/(2)` x - 5

Explanation:

Given f(0) = - 5 and f(4) = - 3 , then we have the coordinate points

(0, - 5) and (4, - 3)

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (0, - 5) and (x₂, y₂ ) = (4, - 3)

m =
`(-3+5)/(4-0)` =
`(2)/(4)` =
`(1)/(2)`

The line crosses the y- axis at (0, - 5) ⇒ c = - 5

y = f(x) =
`(1)/(2)` x - 5 ← equation of line