Question

What’s an equation of the line that is parallel to 3x+y=6 and passes through the point (-2,8)

Answer 1

Parallel lines has same slope.

3x + y = 6

y = -3x + 6

m = slope = -3

Line 2: (-2, 8) , m = -3

(y - y1) = m (x - x1)

(y - 8) = -3(x --2)

(y - 8) = -3(x + 2)

y -8 = -3x - 6

y = -3x - 6 + 8

y = -3x + 2

Answer 2

We know that if two lines are Parallel then both the lines have same Slope.

Given : Equation of 1st Parallel line is 3x + y = 6

this can be written as :

y = -3x + 6

Comparing with standard form : y = mx + c

we can notice that slope = -3

We know that the form of line passing through point (x₀ , y₀) and having slope m is :

y - y₀ = m(x - x₀)

Here the 2nd Parallel line passes through the point (-2 , 8)

x₀ = -2 and y₀ = 8 and we found m = -3

⇒ y - 8 = -3(x + 2)

⇒ y - 8 = -3x - 6

⇒ -3x - y = -2

⇒ 3x + y = 2