line l and and line k are perpendicular. line l has a slope of 3. line k contains the points (5,8) and (2, y). what is the value of y?

Answer 1

line l has slope 3, so line k haas slope -1/3

using the point-slope form of a line,

(y-8) = -1/3 (x-5)
3y-24 = 5-x
3y = 29-x

so, if (2,y) is on the line,

3y = 29-2 = 27
y = 9

Or, without quite so much algebra, knowing that line k has slope 1/-3, we know that y increases by 1 when x decreases by 3.

going from (5,8) to (2,y), x has decreased by 3, so y increases by 1, from 8 to 9.