Answer:
y = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{9}{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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, - 5) and (x₂, y₂ ) = (3, - 6)
m = [tex]\frac{-6+5}{3=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 (1, - 5 ) , then
- 5 = - [tex]\frac{1}{2}[/tex] + c ⇒ c = - 5 + [tex]\frac{1}{2}[/tex] = - [tex]\frac{9}{2}[/tex]
y = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{9}{2}[/tex] ← equation of line
