Answer:
y = -[tex]\frac{1}{2}[/tex] x - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate the slope m, using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
let (x₁, y₁ ) = (4, - 8 ) and (x₂, y₂ ) = (6, - 9 )
substitute these values into the formula for m
m = [tex]\frac{-9-(-8)}{6-4}[/tex] = [tex]\frac{-9+8}{2}[/tex] = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c, substitute either of the 2 points into the partial equation
using (4, - 8 ) for x and y in the partial equation
- 8 = - [tex]\frac{1}{2}[/tex] (4) + c = - 2 + c ( add 2 to both sides )
- 6 = c
y = - [tex]\frac{1}{2}[/tex] x - 6 ← equation of line
