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?

y + 8 = x + 10

Step-by-step 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

= - = - = 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

   y = 8x + 2

Step-by-step 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

11 feet 6 inches and 8 feet 6 inches