Question 940738

find the value for {{{k}}} for which the line {{{2x+ky=16}}} is parallel to y-axis

first find the slope; recall, being parallel to the y-axis means to have a slope {{{undefined}}} or {{{m=1/k}}} where {{{k=0}}}
 
the slope of the given line is: 

{{{2x+ky=16}}}=>{{{y=-(2/k)x+16/k}}
}
& the slope of y-axis is {{{infinity}}} which can be assumed to be equal to {{{-2/0}}}
Since the lines are {{{parallel}}},their {{{slopes}}} are {{{equal}}}.
i.e. {{{-2/k=1/0}}}=> {{{k=0}}}

or, we can solve it this way:

if  the line is {{{parallel}}} to y-axis, then (by definition of the vertical line) we have a {{{vertical}}} line where {{{x}}} is a constant value and {{{y=0}}}; so, whatever value we choose for {{{k}}} if {{{y=0}}} we will have {{{ky=k*0=0}}}