Answer:
x + 2y = - 2
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
Obtain the equation in slope- intercept form
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 ) = (- 2, 0) and (x₂, y₂ ) = (8, - 5)
m = [tex]\frac{-5-0}{8+2}[/tex] = [tex]\frac{-5}{10}[/tex] = - [tex]\frac{1}{2}[/tex]
y = - [tex]\frac{1}{2}[/tex] + c ← partial equation of line
To find c substitute either of the 2 points into the partial equation
Using (- 2, 0), then
0 = 1 + c ⇒ c = - 1
y = - [tex]\frac{1}{2}[/tex] x - 1 ← in slope- intercept form
Multiply through by 2
2y = - x - 2 ( add x to both sides )
x + 2y = - 2 ← in standard form
