Question

Equation of the vertical line passing through $( - 10,4)$ is $x + 10 =$?

Answer 1

A vertical line is a line parallel to the vertical axis or y-axis. So for every point on the line x-coordinate will be constant. And that constant value can be found using the given point.

Formula used:
For a line parallel to the y-axis, x-coordinate will be constant for every point in it.

Complete step-by-step answer:
Given, the point $( - 10,4)$
We have to find the equation of the vertical line passing through this point.
A line is vertical when it is parallel to the y-axis.
For a line parallel to the y-axis, x-coordinate will be constant for every point in it.
So, since the point $( - 10,4)$ belongs to this line we can say that for all points in the line, x-coordinate will be $- 10$.
Thus we can see that this line satisfies the equation $x + 10 = 0$.
$\therefore$ The answer is $x + 10 = 0$

Additional information:
For every line parallel to the x-axis, y-coordinate will be constant for every point. These lines are called horizontal lines. For points in x-axis, y-coordinate will be zero and for points in y-axis, x-coordinate will be zero. For the intersection of the axes, that is the origin, both coordinates will be zero.

Note: Equation of a line can be found in other ways also.
Equation of a line passing through a point $({x_1},{y_1})$ and having slope $m$ is given by $y - {y_1} = m(x - {x_1})$.
Slope of a line is tan of the angle which the line makes with the positive x-axis.
Equation of a line passing through two points $({x_1},{y_1})$ and $({x_2},{y_2})$ is given by $\dfrac{{y - {y_1}}}{{{y_1} - {y_2}}} = \dfrac{{x - {x_1}}}{{{x_1} - {x_2}}}$.