Question 111717
A line passing through (–6, –5) and (–1, y) is perpendicular to a line with slope -5/13 .  Find the value of y.


to find the value of {{{y}}}, you first need to use the given data that this line is {{{perpendicular}}} to a line with slope {{{m[1] =-5/13}}}, so you can calculate a slope {{{m[2]}}}  for your line

we know that if the lines are perpendicular, then : {{{m[1] m[2]= - 1}}}

find {{{slope}}} for line:


{{{m[1] m[2]= - 1}}}


{{{m[2] = - 1/m[1]}}}


{{{m[2] = - 1/(-5/13)}}}


{{{m[2] = - 13/-5}}}


{{{m[2] = 13/5}}} ….this is a slope of a  line passing through (–6, –5) and (–1, y)


we can calculate {{{y}}} using this formula:

{{{m = (y[2] - y[1])/( x[2] - x[1])}}}


{{{13/5 = (y - (-5))/(-1 - (-6))}}}


{{{13/5 = (y + 5)/(-1 + 6)}}}

{{{13/5= y/5 + 1}}}…………………………move {{{1}}} to the left

{{{13/5 – 1 = y/5}}}………multiply both sides by {{{5}}}

{{{13*5/5 – 1*5 = y*5/5}}}………

{{{13 – 5 = y}}}………

{{{8 = y}}}………,,,,,,,,,,,,,,,,,,

*[invoke calculating_slope -6, -5, -1, 8]