Answer:
x - 2y = 10
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 )
Given
x - 2y = 6 ( subtract x from both sides )
- 2y = - x + 6 ( divide both sides by - 2 )
y = [tex]\frac{1}{2}[/tex] x - 3 ← in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
Parallel lines have equal slopes, thus
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (- 6, - 8) into the partial equation
- 8 = - 3 + c ⇒ c = - 8 + 3 = - 5
y = [tex]\frac{1}{2}[/tex] x - 5 ← in slope- intercept form
Multiply through by 2
2y = x - 10 ( subtract 2y from both sides )
0 = x - 2y - 10 ( add 10 to both sides )
10 = x - 2y, that is
x - 2y = 10 ← in standard form
