Question

Explain how one is able to form an equation for a vertical line that passes through the given point; $( - 2,1)$ ?

Answer 1

Hint : Read carefully all the information given in the question. If it is mentioned that the line is horizontal then it means that it is parallel to $x$ - axis and if it says that the line is vertical it means the opposite, that it is perpendicular to the $x$ - axis. An equation consists of an equal to sign. Any straight line can be expressed in an equation like this: $y = mx + c$ .

Complete step-by-step answer :
Let us try to make the equation step by step;
First they have given us:
The point where the line must pass through $( - 2,1)$
Then they have said that the line is vertical and so it means its parallel to the $y$ - axis.
If any line is parallel to a particular axis it just means that; The line has same slope as the axis.
We can take the value of that axis coordinate to be $0$ , the same way in the equation also it will be $0$ .
Here therefore the value of $y$ coordinate will be $0$ .
Our equation is of the general form;
$y = mx + c$ ; where $m$ = slope of graph and $c$ = any constant.
But here it is said that the line is parallel to the vertical axis so the slope of any line parallel to vertical axis does not exist.
So let us consider the equation of a line parallel to $y$ - axis; it will be of a general form given below:
$x = a;\;a =$ $x$ - intercept.
Therefore easily we can put that the equation of line that goes through $( - 2,1)$ and that is vertical is:
$x = - 2$
So, the correct answer is “ $x = - 2$ ”.

Note : We can remember some facts about a linear equation:
- Always the general form of any linear equation is: $y = mx + t$ ; here $m =$ slope and $t =$ $y$ - intercept
- Or we can write a slope point form as : $(y - y') = m(x = x')$
- In these equations depending on the value of $m$ , we can predict the direction of line:
Consider $m$ is negative; then the line moves downward.
Otherwise $m$ is positive; and the line goes upward.