Answer:
y = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{13}{2}[/tex]
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 m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 5, - 4) and (x₂, y₂ ) = (- 1, - 6)
m = [tex]\frac{-6+4}{-1+5}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex], thus
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 (- 1, - 6), then
- 6 = [tex]\frac{1}{2}[/tex] + c ⇒ c = - 6 - [tex]\frac{1}{2}[/tex] = - [tex]\frac{13}{2}[/tex]
y = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{13}{2}[/tex] ← equation of line
