Question

The equation of line j is y + 5 = 2(x − 8. Line k includes the point (-4, -3) and is perpendicular to line j. What is the equation of line k?

Answer 1

y = -
`(1)/(2)` x - 5

y + 5 = 2(x - 8) is in point-slope form

y - b = m(x - a) ( m is the slope and (a, b) a point on the line )

here the slope m = 2

the slope of a line perpendicular to this is equal to -
`(1)/(m)` = -
`(1)/(2)`

line k goes through (- 4, - 3), hence equation is

y + 3 = -
`(1)/(2)`(x + 4) ← in point-slope form

y + 3 = -
`(1)/(2)` x - 2 ( distributing )

y = -
`(1)/(2)` x - 5 ← in slope-intercept form