Answer:
y = [tex]\frac{1}{2}[/tex] x - 5
Step-by-step 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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 5) and (x₂, y₂ ) = (4, - 3)
m = [tex]\frac{-3+5}{4-0}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
The line crosses the y- axis at (0, - 5) ⇒ c = - 5
y = f(x) = [tex]\frac{1}{2}[/tex] x - 5 ← equation of line
