Find an equation of the line that satisfies the given conditions. Through (1, −8); parallel to the line x + 2y = 6?

The typical equation of a line is: y = mx + b → where m: slope and where b: y-intercept


x + 2y = 6 ← this is a line (ℓ1)

2y = - x + 6

y = (- x + 6)/2

y = - (1/2).x + (6/2)

y = - (1/2).x + 3 ← the slope is - (1/2)


Two lines are parallel if they have the same slope. So the slope of the line (ℓ2) is - (1/2) too.

The equation of a line (ℓ2) becomes: y = - (1/2).x + b ← because: m = - 1/2

The line passes through (1 ; - 8), so the coordinates must verify the equation of the line.

y = - (1/2).x + b

b = y + (1/2).x → you substitute x and y by the coordinates of the point (1 ; - 8)

b = - 8 + [(1/2) * 1]

b = - (16/2) + (1/2)

b = - 15/2

→ The equation of the line (ℓ2) is: y = - (1/2).x - (15/2)

y = (- x - 15)/2

2y = - x - 15

x + 2y = - 15

You don't need the "/2".
1 + 2(-8) = 1 - 16 = -15
.. x + 2y = -15 ... goes through your designated point