What is the equation of the vertical line that passes through `(-7,4)`?

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degeneratecircle's profile pic

degeneratecircle | High School Teacher | (Level 2) Associate Educator

Posted on

Vertical lines are the only lines that can't be expressed in the form `y=mx+b.` However, the equations of vertical (and horizontal) lines are very simple. Since this line goes through `(-7,4)` and is vertical, it also goes through `(-7,0),(-7,-12),(-7,23.221),` and in fact `(-7,y)` for every value of `y.` The only thing distinguishing these points is the fact that in all of them `x=-7.`

The equation is `x=-7.`

pramodpandey's profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

let write equation in point slope form

`y-y_1=m(x-x_1)`

where  point is `(x_1,y_1)` and slope is m.

Required line is vertical line i.e. parallel to y axis.let us write point slope equation as

`(y-y_1)/m=x-x_1` ,

slope of y is `oo` ,so above equation reduces to

`x-x_1=0`

Thus equation of vertical line posses through (-7,4) is

x+7=0

x=-7

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