Question

The equation for line j can be written as

y − 6 = -(x + 7)

Perpendicular to line j is line k, which passes through the point (-10, -8)

What is the equation of line k?

Answer 1

y + 8 = x + 10

Explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 6 = -(x + 7) is in this form with slope m = - 1

given the slope of a line m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-1)` = 1

using m = 1 and (a, b) = (- 10, - 8), then

y + 8 = x + 10 ← equation of line k

or y = x + 2 ← in slope- intercept form

Answer 2

Answer: y = 8x + 2

Explanation:

perpendicular means the slopes are opposite reciprocals of each other. perpendicular to: y - 6 = -(x + 7) → m = -1 m⊥ = +1

Input the slope (m⊥ = +1) and the point (x₁, y₁) = (-10, -8) into the Point-Slope formula: y - y₁ = m(x - x₁)

y - (-8) = 1(x - (-10))

y + 8 = x + 10 simplified

y = x + 2 subtracted 8 from both sides