Question

What is an equation of the line that passes through the point ( 1 , − 2 ) (1,−2) and is parallel to the line 6 x + y = 9 6x+y=9?

Answer 1

`\boxed{y=-6x+4}\\`

Explanation:

(a) Slope of parallel line

Your function is

6x + y = 9

y = -6x + 9 Subtracted 6x from each side

slope = -6

The parallel line has slope = -6.

(b) Equation for parallel line

The point-slope formula for a straight line is

y – y₁ = m(x – x₁)

x₁ = 1; y₁ = -2; m = -6

y – (-2) = -6(x - 1)

y + 2 = -6x + 6

y = -6x + 4

The equation for the parallel line is

`\boxed{y=-6x+4}\\`

The graph is a straight line that passes through (1, -2) and has a slope of -6.